Substantial energy return shoe with optimal low-impact springs and tuned gear change

ABSTRACT

The optimized shoe invention comprises five embodiments and two methods to optimize both the performance and comfort of footwear for walking and running and for robotics, prosthetics and orthotics. First, there are three versions of enhanced heel-lift shoes for energy return much higher than that of just “springs in shoes.” Second, to minimize foot impact shoe there are ten enhanced optimal springs with 1% hysteresis loss. Third, for ankle and knee joints there is a rotating-arms enhanced optimal spring. Fourth, said enhanced optimal springs are incorporated into conventional shoes. Fifth, there is an automatic gear change mechanism to change the sole spring stiffness so that the sole is always close to full compression—so that the performance and comfort is always optimal. The optimal force curve method features a pre-loaded constant force curve tuned to a particular use. The shoe tuning method provides precise sole energies by slicing springs.

BACKGROUND

Since the 1980's the holy grail for shoes has been substantial energy return—meaning that a substantial reduction in the metabolic energy cost of running is achieved by an effective coupling of the sole stored impact energy to lift the center of mass of the runner upward and forward during take-off. Simply putting springs anywhere in the sole provides only a few percent energy cost reduction—no matter how energy efficient the springs are. The issues of heel-toe action, ankle and knee action, series support, and timing make this coupling difficult to understand and achieve. Conventional shoes which only feature simple springs in the soles do not provide substantial energy return. Rather, substantial energy return requires enhanced heel-lift which is the goal of the instant invention. However, straightforward designs to achieve enhanced heel-lift are prohibitively complicated. The heel-pop design herein is simple enough to be practical. In addition, low-impact springs reduce the maximum impact force felt by the runner. These optimal springs can be used both in high-performance energy return shoes and in conventional shoes. Finally, optimal performance requires thick soles and full sole compression. The gear change mechanism herein automatically changes the spring system stiffness so that there is always close to full sole compression.

SUMMARY OF THE INVENTION

The optimized shoe invention comprises five embodiments and two methods to optimize both the performance and comfort of footwear walking and running for people and for robotic, prosthetic and orthotic applications. First, there are three versions of enhanced heel-lift shoes (also called heel-pop shoes herein) for significant energy return—that is much higher energy return than what is achievable with conventional shoes. Note (to correct an all too common misconception in the shoe world) that energy return in the instant invention refers to metabolic energy cost reduction, not simply to the coefficient of restitution of the sole springs themselves. That is, the sole energy is used to thrust the runner's center of mass back into the air. This energy return is difficult to understand and very difficult to achieve. Second, to minimize foot impact shoe there are ten enhanced optimal springs. Third, for ankle and knee joints there is a rotating-arms enhanced optimal spring. Fourth, said enhanced optimal springs are incorporated into conventional shoes. Fifth, there is an automatic gear change mechanism to change the sole spring stiffness so that the sole is always is close to full compression—so that performance and comfort is always optimal. This change of sole spring stiffness is referred to herein as “gear change” as a short cut phrase that is easily understandable. The optimal force curve method to minimize foot impact requires optimal springs with a pre-loaded constant force curve, and it requires a means to calculate, measure, and adjust the optimal total sole energy for a particular user for a particular type of running or walking. The shoe tuning method provides a means to measure and adjust sole energy of shoes by precise slicing of 2D sole springs during the manufacture of said shoes or by the use of precise insertable 2D springs—based on the fact that the sole energy absorbed at full deflection by the optimized springs of the instant invention is linearly proportional to a scientifically chosen value of sole thickness. The runner or walker is referred to herein as the user.

The three versions of the heel-pop design herein ensure that virtually all of the foot impact energy is captured and stored during the impact period and then returned via enhanced heel-lift during the heel-lift period. Enhanced heel-lift means that the mechanism lifts only (or primarily) the user's heel (not the toe) by a distance that is substantially greater (by a factor of two to three) than the distance of sole heel compression during the impact period. The critical design feature of heel-pop shoes is that the sole structure below and rearward of the toe joint is spring loaded, and this sole structure flattens out during sole compression. As the runner's weight comes onto the runner's toes, the design ensures that the stored energy is used to lever up and to lift only the runner's heel substantially more than the distance of heel compression. This enhanced heel-lift is referred to herein as heel-pop. It is the best way to achieve substantial energy return. These heel-pop designs are simple, easily manufacturable, and completely novel in the shoe art. That is, although there are a number of shoe patents that claim to feature energy return by virtue of a whole host of types of conventional springs in their soles, in fact none of this prior art provides enhanced heel-lift and none of this prior art provides substantial energy return. The heel-pop benefit is due to the fact that the distance over which the calf muscles are providing heel-lift during heel-lift is roughly three times greater than the distance of heel compression and expansion provided by conventional shoe springs. For conventional shoes, the heel springs act for only a third of heel-lift. Thus, most of the stored heel impact energy is wasted because of the resultant and inherent poor coupling of the heel spring action to the acceleration of the user's center of mass upward and forward during heel-lift. Since the enhanced heel-lift action is doing most of the work of lifting the heel, the calf muscle does not have to work as hard. Thus, the metabolic energy exerted by the calf is significantly reduced, and there is substantial energy return.

The heel-pop mechanism requires that the toe plate be articulated with respect to the footplate. Its compressible sole compresses a greater distance than conventional soles (preferably 1-3 inches), and the footplate section of this sole comprises four sides. The front and rear sides are inclined forward and rotate forward during compression so that the compressible sole is flattened. In the first two versions of the heel-pop embodiment, the front and rear sides are curved springs, and in the third embodiment of the invention, the four sides form a spring-loaded parallelogram which is compressed downward and forward.

With regard to enhanced heel-lift, Rennex U.S. Pat. No. 6,684,531 of Feb. 3, 2004 mentions it almost in passing (his FIG. 21). However, that design was premised on returning most of the foot impact energy at the toe. The enhanced heel-lift was simply an afterthought, and the design was completely impractical. In the instant invention, virtually all of the impact energy goes into enhanced heel-lift, and the instant design is eminently practical. No other prior art was found for the heel-pop (enhanced heel-lift) idea.

Rennex in US patent application 2005/0262725 of Dec. 1, 2005, in FIGS. 9 and 12, anticipates the use of a number of types of springs in linked compressible soles such as a parallelogram sole. These include curved springs which flatten, a v shaped (on its side) floating hinge spring, a curved tension spring, and a conical spring which is similar to the mirrored arch springs of the instant patent. Also, Rennex in U.S. Pat. No. 4,936,030 of Jun. 26, 1990, discloses a parallelogram based compressible sole although that is not obvious or easy to see. With reference to FIGS. 2 and 4 of that Rennex patent, the vertical arms, of the bent 16 in the front and bent lever 25 in the rear, in fact serve as the front and back sides of a parallelogram. There is no articulating toe plate so it could not be used to achieve enhanced heel-lift.

Perenich US application 2013/0125422 of May 23, 2013 discloses a backwards leaning parallelogram with various tension springs between the parallelogram hinges. Although Perenich mentions that the parallelogram might compress forward as well, he teaches nothing in terms of why that might be useful for heel-pop. In fact, the two just-mentioned patents of Rennex completely obviate the claims of Perenich. Furthermore, the springs mentioned by Perenich are entirely impracticable in that these are far too weak, and they add unacceptably to the uncompressed sole thickness. He mentions that the parallelogram could also be forward leaning, but he teaches absolutely nothing as to why it might be forward leaning. That is, he mentions nothing about the heel-pop idea for heel lift, and he mentions nothing about the need for an anti-toe-sink mechanism. Finally, his groundplate is rigid from under the foot to under the toe which makes the heel-pop feature impossible to work. That is, the entirety of the toe region and the foot region must expand together in his design which make heel-pop impossible. And, there is no articulating toe plate. Also, there is no mention of enhanced heel-lift or of the need for an anti-sink mechanism. For all these reasons, his patent application does not anticipate the instant heel-pop invention, and there is not even anything novel in his disclosure. Sugawara U.S. Pat. No. 6,718,655 of Apr. 13, 2004 discloses a “v-hinge” whereby the rear part of the shoe is spring-loaded to bend up (in his FIGS. 21A and 21B), and he discloses in his FIG. 25a and FIG. 25B two v-hinges, whereby both the toe and the heel bend up. This is an admirable effort to get enhanced heel-lift, but it has severe practical problems. First, it only works when the sole fully flattens—otherwise the shoe will be rocking about the joint (or joints) to make the toe go down during toe-off. This is related to the need for and anti-toe-sink mechanism in the instant invention. Another drawback is that the tip ends of his springs rub against the top surface, and also the amount of spring that is bending is very short, which severely limits how strong the spring can be in comparison with the large array of optimized springs in the instant invention.

Regarding the optimal springs of the instant invention, tube springs have been disclosed in shoes since Luthi, U.S. Pat. No. 5,822,886 of Oct. 20, 1998. Other tube disclosures include Keating, US application 2011/0289799 of Dec. 1, 2011 and Lucas, US application 2011/0138652 of Jun. 16, 2011. Oval springs have been disclosed in shoes since Crowley U.S. Pat. No. 4,881,329 of November 1989. Other tube disclosures include Lindh U.S. Pat. No. 4,910,884 of March 1990, Simon U.S. Pat. No. 5,102,107 of Apr. 7, 1992, Hann U.S. Pat. No. 7,788,824 of Sep. 7, 2010, and Nishiwaki—both U.S. Pat. No. 7,779,558 of Aug. 24, 2010 and US Application 2011/0138651 of Jun. 16, 2011. Conical springs have been disclosed in shoes since Cobley U.S. Pat. No. 3,489,402 of January 1970 and McMahon U.S. Pat. No. 4,342,158 of Aug. 3, 1982. Cobley discloses conical springs with internal rubber and he claims that it is possible to get a flat spring rate for h/t=sqrt (2) without rubber and for h/t>sqrt (2) with rubber, where h is the spring height and t is the spring arm thickness. Thus, the claim of a flat spring rate is old in the art. McMahon gives a very erudite and commendable explanation of the possibilities of conical springs in shoes. He also discloses a spring rate which bends over, but for h/t of 1-3. He was the first inventor to use an internal elastomer spring to prevent the spring rate from going to zero, but his goal was to have a continuously linear force curve, not a constant force curve. McMahon was a great scientist and the father of the energy return quest; and, he introduced the instant author to the concept of energy return shoes. His conical springs anticipate the mirrored arch springs of the instant invention and similar springs in a number of recent shoe patents. However, he does not teach how these conical springs can be modified to achieve the optimal force curves of the instant invention.

Patent application US 2011/0138652 of Jun. 16, 2011 by Lucas for Addidas (the famous spring blade shoe) discloses as many blade springs as can be fit in the shoe sole. This sole compresses a minimal amount, ˜¼ inches, which permits many bending blade springs to fit in the footprint. However, the instant invention takes advantage of the fact that it is far better to utilize a minimal number of springs with a thicker sole compression, 1-3 inches in the instant invention, for the following reasons. These few springs (typically two in the instant invention) are more lightweight and easier to manufacture. With regard to the spring blade shoe, the distribution of springs along the entire length of the sole results in less energy return because the rearward springs return their energy even sooner, and, hence, more of that energy is wasted because the coupling between the acceleration of the user's center of mass with said spring action is even worse than if two springs were used (one in the mid section and the other in the heel)—as is most commonly done in conventional shoe designs. These remarks pertain to the use in the instant invention of optimal springs in conventional shoes.

Krstic U.S. Pat. No. 7,089,690 of Aug. 15, 2006 discloses an interesting and notable double-sloped conical spring in which the slope changes partway up the cone. In effect, the first cone section coming up from the center plane acts as a spacer so that the force curve bend-over found in Belleville springs occurs early during compression. The only way this snap-through effect can work (with the greater height needed in a shoe sole, i.e., greater than for the relatively small height for Belleville metal springs) is to use a very compliant material such as TPUs (thermoplastic polyurethanes). This is because the perimeter sections of the cone (at the center plane) must circumferentially expand more and more (˜50%) as the relative spring height increases. Unfortunately, this TPU material is an order of magnitude weaker than fiberglass for mirrored arch springs (refer to the discussion of Tables 1-3 of the instant invention). Also, the use of the de facto spacer of the cone section (corresponding to the first cone section with the first slope) compromises the compression ratio of his spring. Finally, the de facto tension element (around the perimeter) is due to the circular configuration—in which case the advantages of the 2D (cylindrical configuration) mirrored springs of the instant invention are not realized. This 2D advantage is that it is possible to precisely choose and vary the shoe total spring stiffness simply by precisely slicing these 2D springs. Furthermore, these 2D springs are much stronger for their weight and for the space used than for the circular configuration.

The instant invention uses the terminology of a 2D spring and of a mirrored arch spring, as shown in FIG. 10, to describe the 2D equivalent of conical springs, which equivalent is in a cylindrical configuration—as distinguished from the circular configuration of conical springs. Mirrored arch springs have been disclosed since Eliot U.S. Pat. No. 104,718 Jun. 28, 1870 for an auto suspension spring. These have merged or pinched pivots at the center. Whatley U.S. Pat. No. 5,279,051 of Jan. 18, 1994 shows a monolithic mirrored arch spring in his FIG. 4E. This is the first instance found in a shoe. Perenich U.S. Pat. No. 7,290,354 of Nov. 6, 2007 was filed on Apr. 19, 2004 with the earliest cross-reference being Nov. 21, 2002. He shows opposing leaf springs in his FIG. 16 made of carbon fiber. He also shows the equivalent in his U.S. Pat. No. 7,950,166 of May 31, 2011.

The instant invention uses the descriptive terminology of a tensioned mirrored arch spring; this is first shown in monolithic form in FIG. 11 of Cohen U.S. Pat. No. 4,611,412, Sep. 16, 1986. It is first shown with a separate tension element in Lekhtman U.S. Pat. No. 4,492,374 of Jan. 8, 1985, although this is shown as a huge foot-length spring under the foot. These were way to heavy and thick to be of any practical use. Vorderer U.S. Pat. No. 4,843,737 of Jul. 4, 1989 puts a small tensioned mirrored arch spring in the heel using helical springs; he also discloses a planar elastomeric band for the tension spring in his FIG. 8. This invention of Vorderer is very important because it obviates the overly general claims of Greene below. Lucas U.S. Pat. No. 7,013,582 of Mar. 21, 2006 (filed Jul. 15, 2003) and then again in U.S. Pat. No. 7,401,419 of Jul. 22, 2008, shows monolithic tensioned mirrored arch springs in his FIG. 6. Notably he reports a measured internal energy hysteresis value which seems to be about 20% for TPU material. The compression ratio for his spring using this material is poor.

Greene U.S. Pat. No. 8,789,293 of Jul. 29, 2014 discloses a “differential-stiffness impact-attenuation member” with a planar tension spring element, but she makes an improperly general claim of only an “impact-attenuation member”” with a planar tension spring element. I will call her spring a band tensioned flared mirrored arch spring in the terminology of the instant invention. It looks like a wedge in the top view because the walls are spreading out (flared out). Her spring is the same as the tensioned band mirrored arch spring disclosed by Vorderer U.S. Pat. No. 4,843,737, except for the flare out. Thus, her spring is a variation of the tensioned band mirrored arch spring 292 shown in FIG. 20 of the instant invention. She discloses a change in stiffness along her length of spring which corresponds to the width of the 2D springs in the instant invention (the flare out). She discloses only mirrored arch springs for which the side length of the arch is changing along her length dimension (see her FIG. 1A and FIG. 1B). This corresponds to the just mentioned stiffness change along the length. In fact, there are other ways to change the stiffness, and she should not be allowed to claim these without teaching them. To restate—her spring width and stiffness change along her spring length. This is the only novel teaching in her patent, but these two related disclosures (width and stiffness change) are not used to narrow her base claims—which, hence, are improperly general and invalid in view of Vorderer above. In addition, Greene mentions that the tension element might be slightly curved or undulating, but there are numerous examples in the prior art for such tension elements. Thus, she can properly claim her change in width (stiffness), but only for a monolithic (unitary spring). In fact, in an earlier patent in this same thread of cross-referenced patents, namely Greene U.S. Pat. No. 8,539,696 Sep. 24, 2013, she does narrow her base claim with the differential-stiffness feature. This is more valid than for U.S. Pat. No. 8,789,293 just above, but it should only be claimed for a unitary differential-stiffness spring—in which case, one can still use separate springs to achieve the equivalent result and to overcome even this proper claim. A less obvious, but still valid reason that Greene's claim is invalid has to do with the following. Herr U.S. Pat. No. 6,029,374 of Feb. 29, 2000, discloses, in the discussions of his FIG. 25 and FIG. 29, the use of one or more springs with different stiffness at various locations about the shoe (likewise for the below “varying stiffness” prior art). Herr discloses leaf springs which are an example of 2D springs in that they have the identical cross sectional shape across their width. One can make the case that a 2D spring is equivalent to a number of sliced 2D springs positioned side by side. In that case, Greene's disclosure of stiffness variation along the her length (or my width for 2D springs) of her spring is obvious and not patentable because a spring can be an assembly of a number of side-by-side strips—each of which has a constant stiffness across its width (her length) and each of which may have its own particular stiffness. Thus, this is the argument that Greene cannot claim even the stiffness variation when her spring is unitary (monolithic). Moreover, Greene also discloses that her claims cover separated springs. That is definitely incorrect in view of Herr (above.) In fact, it is more convenient to manufacture the 2D mirrored arch springs of the instant invention, which have constant dimensions of the side walls across the across the (instant invention) width of the spring. To vary the stiffness across the width of the shoe, it is preferable to simply use a separate spring strips with different stiffness distributed across the shoe width. This stiffness can varied either by virtue of geometry, material, or sidewall thickness. Finally, Herr U.S. Pat. No. 6,029,374 of Feb. 29, 2000, discloses, in the discussions of his FIG. 25 and FIG. 29, the use of one or more such springs with different stiffness at various locations about the shoe. Thus, Greene's disclosure of stiffness variation along the length of her conical spring is obvious and not patentable because a spring can be a composite of a number of side-by-side strips—each of which has a constant stiffness across its width (her length). And in addition, not only does Greene not mention in her claims her novel matter, the differential stiffness change, but she also broadens her claim for the tension spring as any concavity spring with a tension element—which is clearly invalidated by Vorderer. In that case, Greene should only be able to claim her particular novel versions of the tensioned mirrored arch spring.

Smaldone U.S. Pat. No. 8,720,085 of May 13, 2014 is a continuation of Smaldone U.S. Pat. No. 7,314,125 of Jan. 1, 2008. It was filed on Sep. 27, 2004. She discloses just a few particular mirrored tensioned designs with shafted pivots. She claims a general tensioned mirrored arch spring, which is invalid in view of Vorderer. The only novel matter here is that she discloses a monolithic pivot with a pocket receptacle to hold a planar tension element. This has the disadvantage that the edges of the pocket are levering together like a nutcracker to impinge the planar tension element, which is likely to damage it so it will break. Also, since the TPU-like planar material they are using is very compliant, it is likely that the ends will pull through. And, she discloses a band tension element that wraps around the mirrored arch spring section to act as a tension element. This uses up vertical space unnecessarily. However, none of this novel matter is claimed, so this patent does not prohibit the tensioned mirrored arch springs of the instant invention because the base claims are invalid. Her patent certainly does not prevent the patenting of (1) other means to hold the tension element, (2) other tension elements, or (3) other pivots connecting the various arch and tension elements of the novel tensioned mirrored arch springs of the instant invention.

Aveni U.S. Pat. No. 8,225,531 of Jul. 24, 2012 discloses a number of springs of distinct design, some with shear resistance in a particular direction. His base claim is for the use of one or more such springs at various locations about the shoe with various stiffness values. His entire base claim is invalidated in view of the “varying stiffness” prior art below which also discloses shear resistant springs of various stiffness values in various locations of the sole. His only novel features are the particular types of shear resistant spring, and he would have to write a separate patent for each of those with appropriately narrow claims. He also discloses particular shear resistant springs which are shear resistant in only one direction. In fact, there are other shear resistant springs in the shoe art; all of the 2D springs disclosed in the instant invention are shear resistant across their widths. Therefore, any general claim that Aveni might make for shear resistant springs is invalid. He can only claim those of his specific designs that happen to be novel. All of the enhanced optimal springs of the instant invention are superior to and patently distinct from any of the springs disclosed by Aveni, so his patent does not invalidate the instant invention. The complete prior art for multiple springs in various locations with different stiffness values are the following: Rennex U.S. Pat. No. 4,936,030 of Jun. 26, 1990 filed Nov. 8, 1988 disclosed multiple spring locations on sides and in front and back of sole with varying stiffness (he mentions their use to deal with pronation); Miller U.S. Pat. No. 5,628,128 of May 13, 1997 filed on Jun. 7, 1995 (his claim 6); Miller U.S. Pat. No. 5,625,963 of May 6, 1997 filed on Nov. 1, 1994 (his claim 3); Healy U.S. Pat. No. 6,568,102 of May 27, 2003 filed on Feb. 24, 2000 (his claim 7); Crary U.S. Pat. No. 6,457,261 of Oct. 1, 2002 filed on Jan. 22, 2001; Herr U.S. Pat. No. 6,029,374 of Feb. 29, 2000, and Houser US Application 20020038522 filed on Apr. 4, 2002 (which also has these springs at varying orientations). This prior art will be referred to as the “varying stiffness” prior art. Of these, the ones that are also shear resistant are those of Miller. These all pre-date Aveni's patent. Finally, Aveni U.S. Pat. No. 8,261,469 of Sep. 11, 2012, filed on Jul. 21, 2006, claims multiple springs that are oriented at different angles. This claim is obvious and never should have been allowed. In fact, Houser US Application 20020038522 filed on Apr. 4, 2002 (which pre-dates Aveni's file date of Jul. 21, 2006) discloses springs at varying orientations and at various stiffness values. Moreover and more importantly, the positioning of springs at various locations and orientations is necessarily and totally obvious. By allowing these obvious claims, the examiner now prevents any other inventor from incorporating valuable, patently distinct springs in the future in their patents if these springs are oriented at various angles. Even worse, these claims retroactively clash with in the earlier patent of Houser that has been awarded, which discloses positioning of springs at various locations and orientations. And, any other earlier springs which may have been oriented at various angles would be retroactively disallowed. That is wrong and will not hold up in court. There are numerous cross-referenced patents (27) and patent applications leading up to the patents discussed above by Greene, Smaldone, and Aveni. These have virtually the same matter and figures so the same conclusions about the validity of those related patents apply. They are listed in the information disclosure form of the application of the instant invention.

Klassen U.S. Pat. No. 8,707,582 of Apr. 29, 2014 discloses a several “toggle linkage” springs. This was filed on May 30, 2008 based on provisional patents going back to Sep. 6, 2007. Refer to FIG. 19 of the instant invention to see some of these configurations. The idea in general is that the action of a pair (or four links if the paired linkage is mirrored to have four sides) of hinged rigid links oppose the motion of the resilient elements to which they are connected; and, their configuration may be compressive or in tension. As the toggle linkage spring flattens, the opposing forces of the link elements and the resilient elements become more aligned until the vertical spring force goes to zero. This basic design is old, and perhaps ancient, in the art. Klassen only teaches the use of tension resilient springs, but the instant invention also teaches compressive resilient elements, which is completely novel. Klassen's main embodiment (incidentally, the only one claimed) is for a circular configuration. The tension element is a resilient ring around the exterior of a rigid opposing disc assembly although that tension element is not even needed. That is, with reference to Belleville springs (also old in the art), in a circular configuration the circumferential expansion of the spring provides resistance to flattening of the conical discs. This circumferential expansion is also why Klassen requires radial slots, which however make the manufacture of his claimed disc embodiment difficult and more expensive. In his same base claim, there is a damper to prevent the spring from bottoming out and to dissipate energy. With reference to Klassen's FIGS. 9 and 10, his arguments for the benefits his dampers are misguided and misleading for the following reasons. An analysis—of the time dependent force distribution (from heel to toe) as related to the knee and ankle action of running—as applied to the energy return of the instant invention—is very involved and complicated. His arguments do not reflect such a thorough analysis, so it is not surprising that his conclusions are mistaken. Impact energy dissipation (damping) is a disadvantage, not an advantage. The delayed energy return of his heel spring is totally wasted as it expands in the air. Also, his analysis of the coupling of the heel spring to propel the runner back into the air is completely mistaken. Finally, there is no need for the heel (or the full sole) force to go to zero for the middle portion of the stance phase. Since the heel-pop shoe provides a geometric constraint that the front and rear parts of the sole must compress together while the footplate remains level, such a delay is even more unnecessary. Rather, the force curve should remain constant, or it should even be slightly increasing throughout compression. The heel-pop mechanism of the instant invention actually does couple optimally with the knee and ankle action for energy return, and it is explained in detail in the discussion of FIGS. 1-9 of the instant invention. Also, Klassen's material mentioned for his resilient ring is delrin which has detrimental hysteresis energy loss. Klassen also discloses toggle linkage spring designs in cylindrical configuration with necked down pivots and links (also not claimed). One of these (in Klassen's FIGS. 50-52) uses two loops 290 as compressive elements of a toggle linkage spring. These are the rings which compress as the spring flattens to store impact energy. This is a valid and interesting design, but the spring strength per unit area of the shoe sole is very limited because only a small volume (of the rings) is being used to store the impact energy. Thus, the height of these springs would have to be so high that the compression ratio would not be good. Also, again, the material delrin mentioned by Klassen is not optimally strong and it has energy hysteresis loss. Finally, compression of a ring is not an optimal design for energy storage. Another design in his FIGS. 37-40 uses a tensioned band for the resilient element. This is the best design in his patent, but he does not even claim it. Furthermore, just because a force curve is constant does not mean that foot impact energy is still being absorbed for that final portion of sole compression, which is vitally important for the shoe sole application. Note that the auxiliary springs of the instant invention continue to store sole impact energy even while the linkage-spread springs are no longer storing this energy. And, Klassen does not explain or even mention the reduction of the maximum impact force point with the use optimal springs, which reduction is a main benefit of the instant invention. Also, Klassen discloses the same monolithic pivot, with a pocket receptacle to hold a planar tension element, that Smaldone discloses in U.S. Pat. No. 8,720,085 of May 13, 2014. (See the remarks above about Smaldone for a critique of this pocket receptacle design.) Finally, Klassen's springs are not nearly strong as the fiberglass optimal springs of the instant invention. And, their construction is far more complicated and difficult, and they force the uncompressed sole much higher off the ground. Another design is that of Lekhtman US 2010/0223810 of Sep. 9, 2010 who discloses floating hinge springs monolithically connect to a sole plate. These are similar to the curly v-springs of the instant invention, and floating hinge springs are old in the art so this patent does not restrict the use the curly v-springs of the instant invention.

With regard to the capability of manufacturing or adjusting the stiffness of a shoe, the following prior art was found. Chu US application 2006/0075657 of Apr. 13, 2006 has an adjustable heel spring. DiBenedetto U.S. Pat. No. 8,234,798 of Aug. 7, 2012 has a heel spring which is compressed by an electric powered worm gear based on impact sensor information fed to an on-shoe microprocessor. The idea of compressing a spring to increase its stiffness for greater shoe impact is completely flawed because the compression distance is reduced and the deleterious result is to increase the stress on the runner's foot and leg. In contrast, the optimal force curve method of the instant invention requires that the compression distance always be maximized, and the automatic “gear change” of the instant invention is instantaneous. Lyden US application 2008/0060220 of Mar. 13, 2008 goes to enormous lengths to show he has a general method to customize a shoe for any individual shoe user, but his application is devoid of enabling, teachable detail, and it does not define what optimal is as it is defined in the instant invention. Nurse US application 2011/0047816 of Mar. 3, 2011 discloses a general method to adjust “stiffening members” and “tunable members” without teaching anything about what these adjustable members might be, how they might be adjusted, or on what basis they might be adjusted. As was the case for Lyden above, this is an attempt to claim an overly general and obvious invention (capability) without doing the hard work needed to actually design real inventions. As such, it is an attempt to prevent diligent inventors from being awarded patents that actually do work and that actually are based on the teaching of the required knowledge and design base needed for real inventions. Wilkinson US application 2006/0174515 of Aug. 10, 2006 has a lever with a movable fulcrum to change spring stiffness. This is a commendable goal, but not a practical design.

With regard to the use of insertable “cartridge-type” shoe springs, Lindqvist U.S. Pat. No. 8,056,262 of Nov. 15, 2011 discloses a leaf spring insert. Weiss U.S. Pat. No. 7,802,378 of Sep. 28, 2010 inserts a compressible core, Meschan U.S. Pat. No. 7,726,042 of Jun. 1, 2010 inserts a screw-in-able helical spring, and Leedy U.S. Pat. No. 8,006,408 of Aug. 30, 2011 inserts circular plug springs. Smaldone U.S. Pat. No. 7,082,698 of Aug. 1, 2006 discloses insertable tubular plug-in springs. None of these have the advantages of optimal springs of the instant invention, nor do they instantaneously and automatically “change gears”—which refers to changing the shoe spring stiffness values.

With regard to sensor-enabled automatic gear adjustment, Riley U.S. Pat. No. 7,771,320 of Aug. 10, 2010 discloses shoe sensors for workout optimization. Berner US application US 2010/0037489 of Feb. 18, 2010 discloses how sensors can be inserted or incorporated in shoes. Both of these patents are assigned to Nike. Regarding the incorporation or insertion of sensors in shoes per se, the just-above comments for Lyden and Nurse apply here as well. These are just attempts to block real inventions with actual teaching matter from being patented. The use of shoes sensors is obvious and old in the art. Regarding the matter of the use of shoe sensors for workout optimization, that is outside of the purview of the instant invention.

The springs of the above prior art are not nearly strong as the fiberglass optimal springs of the instant invention, and this prior art teaches nothing about why fiberglass is by far the best material for shoe applications, in terms of strength. Rather, the above prior art teaching is restricted to discussion of injection moldable materials such as the thermoplastic elastomer PEBAXX 5533. That is, they ignore the fact that a fiberglass product can also be mass produced. The discussions of Tables 1-3 of the instant invention substantiate the use of fiberglass as the preferred material for the springs of the instant invention. A very interesting candidate material is disclosed by Pratt in U.S. Pat. No. 7,906,191 of Mar. 15, 2011. He discloses a composite material in which the fibers in a particular layer are laid down in sinusoidal waves transversely oriented within the plane of the layer. This means that a composite of wavy fibers can be stretched considerably without breaking the fibers. For fiberglass the elongation limit is of the order of ˜4-5%, and for carbon fiber the elongation is ˜1-2%. That is not enough for the requirements of tension bands 302 herein. By incorporating the wavy structure it is possible to increase the amount significantly. However, Pratt's goal was to provide damping of structures made of his wavy composite material for bending applications, not for stretching. Quoting from Pratt's patent—“The terminology CWCV (continuous wave composite viscoelastic) will be used to define a composite structure which uses at least one layer of wavy composite material having viscoelastic properties (or anisotropic viscoelastic′); or at least one layer of wavy composite material combined with at least one layer of viscoelastic material either in a sandwich construction or adjacent construction.” Also, “Damping is induced in the structure primarily by the differential shearing of the viscoelastic layer by the wavy composite laminate. This shearing induces elongation of the long chain polymers in the viscoelastic which in turn generates heat, causing energy loss in the structure. This energy loss accounts for the primary source of damping in the structure.” Of course, for the purpose of the instant patent, the goal is to have a minimum of damping or energy dissipation. However, it is possible to make a continuous wavy composite without the viscoelastic layers. This then is the preferred material for the tension bands 302 in FIG. 7, FIG. 20, and FIG. 22 herein. The important advantages are the strength and the low energy hysteresis loss (sans the viscoelastic layers). It may be possible here to use carbon fiber composite as well as fiberglass fiber. Another issue is that the optimal springs herein constitute a class of springs which are generically referred to as arch springs. Each arm of these springs is initially curved and then is flattened until straight, during compression. There are a number of permutations in terms of how these curved arms are combined: including one-sided, two-sided (the arch), and mirrored. However, all these permutations have the same force curve.

The arch springs focused on herein are in a cylindrical geometry which provides for much improved lateral stability across the width of the shoe and which distributes the strain energy of the spring more uniformly over the entire shoe print. However, the modifications of the instant invention needed to achieve an optimal force curve can be easily applied to a circular geometry in the manner obvious to one of ordinary skill in the art. The other point of distinction for the arch springs herein is that the arms of the arch springs can be varied in terms of material, shape, taper, means of connection, and internal geometry—so as to achieve the optimal force curve. In short, there is nothing in the prior art like the enhanced optimal arch springs of the instant invention.

DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic side view at heel-strike of the linkage-spread curved-spring heel-pop shoe which is the first version of the first embodiment of the invention with enhanced heel-lift for substantial energy return.

FIG. 2 depicts a schematic side view at mid-stance compression of the linkage-spread curved-spring heel-pop shoe.

FIG. 3 depicts a schematic side view at toe-off of the linkage-spread curved-spring heel-pop shoe.

FIG. 4 depicts a schematic side view at heel-strike of the curved-spring heel-pop energy return shoe which is the second version of the first embodiment of the invention with enhanced heel-lift for substantial energy return.

FIG. 5 depicts a schematic side view at mid-stance compression of the curved-spring heel-pop energy return shoe.

FIG. 6 depicts a schematic side view at toe-off of the curved-spring heel-pop energy return shoe.

FIG. 7 depicts a schematic side view at heel-strike of the parallelogram heel-pop shoe which is the third version of the first embodiment of the invention with enhanced heel-lift for substantial energy return.

FIG. 8 depicts a schematic side view at mid-stance compression of the parallelogram heel-pop shoe.

FIG. 9 depicts a schematic side view at toe-off of the parallelogram heel-pop shoe.

FIG. 10 shows schematic side views of the mirrored arch spring and the curly v-spring.

FIG. 11 shows schematic side views of a pre-loaded curved spring and a mirrored arch spring.

FIG. 12 shows a study of optimized force curves for springs.

FIG. 13 shows schematic side views of an internal linkage mirrored arch spring.

FIG. 14 shows schematic side views of linkage-spread curved springs.

FIG. 15 shows a schematic cut-out side view of a monolithic mirrored spreader linkage.

FIG. 16 shows schematic side views of a kite-end curved spring at various levels of compression.

FIG. 17 shows schematic side views of configurations for arrowhead, kite-end and double-link spread curved springs.

FIG. 18 shows schematic side views of a monolithic tensioned mirrored arch spring.

FIG. 19 shows schematic side views of torque-lift configurations for optimal springs.

FIG. 20 shows schematic side views of a tensioned band mirrored arch spring.

FIG. 22 shows schematic side views of monolithic tensioned linkage configurations.

FIG. 21 shows schematic side views of two tensioned linkage configurations.

FIG. 23 is a schematic side view of a monolithic nested tensioned linkage spring.

FIG. 24 shows schematic side views and a top view of optimal springs in a conventional shoe.

FIG. 25 shows a schematic top view of possible spring locations for a shoe.

FIG. 26 shows schematic views for “gear change” in shoes.

FIG. 27 shows schematic side views of a tensioned linkage rotating arms curved spring.

DETAILED DESCRIPTION OF THE INVENTION

FIGS. 1, 2, and 3 depict schematic side views at heel strike, mid-stance, and toe-off of the linkage-spread curved-spring heel-pop shoe, which provides enhanced heel lift—which in turn provides substantial energy return. This is the first version of the first embodiment of the invention, namely the heel-pop energy return shoe (featuring enhanced heel-lift). The sole compression due to the impact force of running is resisted by a spring system. After the sole is compressed, the runner's toe weight pins down the toe plate of the sole while the combination of the spring system and the sole's parallelogram-like geometry causes the heel section to be lifted upward into the air by an enhanced distance which is of the order of two to three times the compression distance of the heel during the period between heel-strike and mid-stance.

The basic structure of linkage-spread curved spring heel-pop shoe 51 features linkage-spread curved spring heel-pop sole 73 which comprises the following elements (which form a monolithic structure with pivots which are necked-down living hinges). Front footplate link 67 is hingeably connected to mid footplate link 53 which is hingeably connected to rear curved spring 62 which is hingeably connected to groundplate link 57 which is hingeably connected to front curved spring 60 which completes the closed four-sided linkage by pivotally connecting to both front footplate link 67 and mid footplate link 53 via front mono top 4-link pivot 61. These pivotal connections are also made via rear mono top 3-link pivot 59, rear bottom merged pivot 59, and front bottom merged pivot 65. End footplate link 55 is the monolithic continuation of mid footplate link 53. These various living hinges can as well be achieved with conventional cylindrical hinges using shafts and bearings—with design penalties of weight, space, noise, and cost. Shafts and bearings force the sole height to be higher because the load forces are substantial, and, hence, the bearing diameters are larger. The shapes of the necked-down living hinges are indicated in the figure. These are designed to permit the necessary rotations of the various elements, one with respect to the other. As will be shown later in the discussion of FIG. 25 and Tables 1, 2, and 3, fiberglass composite is stronger by a factor of 10 than carbon composite and by a factor of 16 than PEBAX 5533—for the 2D curved springs which flatten, herein. Therefore, fiberglass composite is preferred because the strength advantage corresponds to a light weight advantage. Accordingly, fiberglass composite is the preferred material for the spring/link monolithic linkages in FIG. 1—with the exception of double linkages 131 which are used just as links and not as springs—in which case TPU-like materials are preferred because they can be injection molded. By making the length sections thicker of the link parts of the spring/link monolithic linkages, they can function as links. Double linkages 131 can be made of injection moldable materials such as pellethane or PEBAX 5533.

Double linkages 131 act to spread both rear curved spring 62 and front curved spring 60 so as to straighten out during sole compression. This combination of linkage and curved spring is referred to herein as an internal linkage one-sided curved spring and is discussed in detail for FIG. 14 below. Suffice it to say here, the linkage spreading action serves to bend over the force curve of this sole spring system, as is further discussed in detail for FIG. 11 and FIG. 12 for optimal springs. These optimal springs can reduce the maximum impact force point by as much as 40%. Top adjust spring 132 controls and modulates the onset of this linkage spreading which can eventually bend the spring system force curve over to approach zero. One or more adjust springs 133 allow said total force curve to remain approximately constant near full sole compression, as the force curve, due to the just mentioned internal linkage one-sided curved springs in the front and back, goes to zero.

Anti-toe-sink mechanism 74 comprises spring plate 52 which is fixably attached to ladder stop 35. Note that while spring plate 52 acts as a virtual continuation of groundplate link 57, they are in fact separate. This permits groundplate link 57 to rotate upward as shown in FIG. 3 during heel-lift, while spring plate 52 remains pinned to the ground by the weight of the force imparted by the toe of the runner during toe-off. Front footplate link 67 has ladder steps 36 on its front side. Front footplate link 67 is hingeably connected to spring plate 52 via toe curved spring 69 and via toe spring merged pivot 71. Toe plate 7 is hingeably connected to mid footplate link 53 via front mono top 4-link pivot 61, and it has toe stop 20 fixably attached to its mid section so that toe stop 20 protrudes downward. Toe plate 7 is biased upward by toe spring 21 which connects it to front footplate link 67.

With reference to FIG. 1 at heel strike, FIG. 2 at mid-stance, and FIG. 3 at toe-off and accordingly, linkage-spread curved spring heel-pop shoe 51 functions as follows. During foot impact, as linkage-spread curved-spring heel-pop sole 73 compresses, rear curved spring 62 and front curved spring 60 bend to gradually flatten against groundplate link 57. Top adjust spring 132 (optional) quickly compresses to gradually spread out double linkages 131, which in turn straighten out rear curved spring 62 and front curved spring 60. At a prescribed compression, mid footplate link 53 begins to load adjust spring 133, in parallel with the loading of rear curved spring 62 and front curved spring 60, thereby maintaining the force curve to be approximately constant for the remainder of compression. This adjustment by adjust spring 133 is needed because the spread loading of rear curved spring 62 and front curved spring 60 by double linkages 131 results in the vertical force between the center of double linkages 131 and mid footplate link 53 to go to zero as the mechanical advantage of the action of double linkages 131 goes to infinity as they straighten out.

Also, during compression until mid-stance, toe spring 21 maintains toe plate 7 to be slightly rotated above front footplate link 67 so that toe stop 20 does not impinge ladder steps 36. And, since toe curved spring 69 has the same shape and pivot as front curved spring 60, front footplate link 67 remains approximately horizontal and aligned with mid footplate link 53. Note that toe curved spring 69 is only just strong enough to maintain this alignment. The intention is to minimize the compression energy stored in toe curved spring 69 so that the maximum compression energy is stored in the other main spring elements which provide energy for enhanced heel-lift.

Note in FIG. 2 at maximum compression (not full in this example) that the various springs will have compressed (or flattened) as far as they can. Also, the entirety of the top link elements, including front footplate link 67, have moved forward. Thus, toe stop 20 has stayed above ladder steps 36. Also the vector for the total resultant force of the runner's foot on the shoe continually moves forward. When the runner pushes her toe down, toe plate 7 rotates down so that top stop 20 impinges the adjacent one of ladder steps 36, and thus toe plate 7 cannot move down. During heel-lift, only the rear part of the sole assembly expands as the spring system pushes apart mid footplate link 53 away from groundplate link 57. Since the runner's weight is transferring forward to top plate 7, the top section of front curved spring 60 remains pinned to spring plate 52 which is pinned to the ground. However, the rear section of front curved spring 60 is free to curl up. The result is that the runner's heel is lifted up to achieve enhanced lift. That is, virtually all of the stored impact energy is thus used for heel-lift. After toe-off, the sole returns to its original expanded configuration, as shown in FIG. 1—by virtue of the expansion of the various elements of the spring system, including toe curved spring 69 which re-positions spring plate 52 to be adjacent to and aligned with groundplate link 57. This enhanced heel-lift is the essential and novel function of all versions of the heel-pop embodiment of the invention.

Note that ladder stop 35 must be located outside of toe plate 7 so that it does not interfere with its compression—likewise for toe curved spring 69, and front curved spring 60. Also, the various spring elements extend across the width of the shoe. As will is discussed below for FIG. 25 for conventional shoes, these spring elements are very strong so they do not need to extend all the way across the width of the shoe. In that case a bridging plate is incorporated above and fixably attached to linkage-spread curved-spring heel-pop sole 73 to fixably position the various separate width sections of the spring system elements. Likewise is true for the bottom sides of these spring system elements. Also, since the top side of linkage-spread curved-spring heel-pop sole 73 translates forward with respect to its bottom side, any springs which act directly between the top and bottom sides must allow this forward translation. This is accomplished for adjust spring 133 by positioning it in a slightly backwards rotated orientation before it starts to be compressed. The particular type of spring shown in FIG. 1 is mirrored arch spring 80 of FIG. 10. And, for the case when the impact force of running or walking is always pretty much the same, anti-toe-sink mechanism 74 is not required, but the heel-pop action still takes place. This case is included in the claims of the instant invention. Finally, for any versions of the heel-pop embodiment herein, an alternative trigger other than the toe pushing down can be used to rotate toe stop 20 down to impinge ladder steps 36. This alternative trigger is the onset of heel-lift, and it would work for running robots that do not have toe “muscles”, so to speak. A simple spring-loaded lever at the bottom rear end of groundplate link 57 can be connected to the rotating action of toe plate 7 so that toe plate 7 rotates down when the bottom rear end of groundplate link 57 is lifted.

FIGS. 4, 5, and 6 depict schematic side views at heel strike, mid-stance compression, and toe-off of curved-spring heel-pop shoe 50 which is the second version of the first embodiment of invention. Front curved spring 60 and rear curved spring 62 comprise a monolithic fiberglass spring structure with spring base 70, which connects them and which in turn is strengthened and protected from the ground by the attached groundplate 5. It is also possible to clamp down the bottoms of front curved spring 60 and rear curved spring 62 to groundplate 5, in which case they do not form a monolithic spring structure. All of the above elements extend across the width of the shoe or across smaller widths as shown in FIG. 24 which discusses optimal springs for use in conventional shoes. Even so, all of these optimal springs (arch springs, mirrored arch springs, and curly v-springs to be discussed below in detail) can be sliced and used in two or more locations across the width of the shoe sole.

Front hinge 64 and rear hinge 66 connect these curved springs to footplate 3. At heel strike, these curved springs flatten out as shown in FIG. 5, and footplate 3 moves forward and downward with respect to groundplate 5. Shoe upper 1 is attached to footplate 3 in such a manner that the runner can freely flex her toe. Toe plate 7 is hingeably connected to footplate 3. Toe stop 20 is fixably attached to toe plate 7 in its mid section, and it extends somewhat below toe plate 7. Toe parallelogram 54 comprises the following elements: top toe link 68 and front toe curved spring 69. Front curved spring 60 serves as the rear element of toe parallelogram 54. As such it is the shared link which makes enhanced heel-lift possible. Note that the shape of toe curved spring 69 is the same as the shape of front curved spring 60 to ensure that top toe link 68 remains horizontal during compression—to ensure that toe stop 20 does not engage ladder steps 36 prematurely. Spring plate 52 serves as the bottom element of toe parallelogram 54. Note that even though this bottom element, spring plate 52, is separated from groundplate 5 and hence from the rear toe parallelogram element (front curved spring 60), during compression both spring plate 52 and groundplate 5 are firmly pushed down against the ground so that these two elements behave as if they were one continuous rigid element. This means that toe parallelogram 54 behaves like a parallelogram.

As with the heel-pop shoe of FIGS. 1-3, for the current version of FIGS. 4-6, anti-toe-sink elements are located outside toe plate 7 on both sides, as shown in FIG. 25. Ladder stop 35 is located adjacent to toe plate 7 so that toe plate 7 is free to descend during sole compression. Toe stop 20 is located on and adjacent to toe plate 7 so that toe stop 20 is directly above ladder stop 20. Toe spring 21 weakly biases toe plate 7 to stay above top toe link 19. Spring plate 52 is fixably attached to the bottom of ladder stop 35, and it extends across the bottom of the front sole so as to protect front curved spring 60 from the ground during sole compression. Note that spring plate 52 is not attached to ground plate 5; this is important because it allows spring plate 52 to separate from groundplate 5 during heel-lift. Toe parallelogram 54 and ladder stop 20 are hingeably connected to both footplate 3 and toe plate 7 only by front hinge 64 and by toe spring 21.

Accordingly, 2^(nd) anti-toe-sink mechanism 75 comprises toe spring 21, toe plate 7, toe stop 20, toe parallelogram 54, and ladder stop 35. Its purpose is to prevent the runner's toe from sinking down during toe-off for the case when the sole is not fully compressed. If the toe were allowed to sink, it would be like running in sand and highly objectionable. As such, anti-toe-sink mechanism is the crux of the invention. It works as follows. During the first half of toe stance (provided the runner is landing heel first), the foot impact is shared by the heel and the ball of the foot (just behind the toe joint). But, the toe is not weighted until toe-off. During compression, toe spring 21 is strong enough to prevent toe stop 20 from rotating down to impinge the closest step on ladder stop 35. Ladder steps 36 of ladder stop 35 are positioned so that only when toe plate 7 rotates down below top toe link 68, does toe stop 20 impinge the closest one of ladder steps 36, thereby preventing toe sink. Note that this scheme works only when footplate 3 moves forward with respect to groundplate 5 during sole compression. Also, 2^(nd) anti-toe-sink mechanism 75 allows the runner to run on his toes rather than just on his heels.

FIG. 6 shows how energy return is achieved. First, look at FIG. 5 at full sole compression. Note that front toe curved spring 69 is almost flat on the ground. Just before heel-lift, the user's weight shifts over onto toe plate 7, rotating it downward and overcoming the bias of toe spring 21, so that toe stop 20 impinges the nearest ladder step 36 to prevent toe sink. At the same time, front hinge 64 has been prevented from moving further downward by the action of the compressed spring system. Also, top toe link 68 has been pushed all the way down. And, note that toe plate 7 has been stopped, in this case from being horizontal at the end of its descent, by the bottom ladder step 36 of ladder stop 35. This option allows the runner to push off a slightly higher point and to thereby increase his stride slightly. Of course, it is optional to make the bottom step lower. At this same time of the beginning of toe-off, the runner's heel begins to lift. This allows both front curved spring 60 and rear curved spring 62 to curl up and return to their original uncompressed shape. As this happens, only the runner's heel is impelled into the air; hence, we have enhanced heel-lift and optimal, substantial energy return. Note that all of the foot impact energy has been stored in the two curved springs, and all of the impact energy is returned to lift the heel. Since this heel-lift force acts in parallel with the action of the runner's calf during toe-off, energy return is optimized. Also, this heel-lift distance is substantially greater than the heel deflection distance during heel compression (by a factor of two to three).

It is possible to taper the thickness profile of the sole thickness so that the thickness is somewhat lower at the front. This can be accomplished by increasing the curvature of front curved spring 60 with respect to that of rear curved spring 62 so that the whole of footplate 3 moves forward the same distance and in such a manner that the two springs will not constrain each other from fully flattening during heel compression. However, a thinner front sole thickness results in a smaller amount of heel-lift. Also, the thickness of the curved-spring heel-pop shoe of FIGS. 1-3 can be decreased say to 1.5″ or even to 1″. However, the amount of heel-lift (and, hence, the energy return) will be smaller. And, the thickness can be larger for ultimate performance shoes—perhaps to three or four inches.

Along with the first version of FIGS. 1-3, this second version of the first heel-pop embodiment of the invention, namely curved-spring heel-pop shoe 50 of FIGS. 4-6, is considered preferable to the third version yet to come, parallelogram curved-spring shoe 2 of FIGS. 7-9, for the following reasons. The parallelogram of FIGS. 7-9 serves two functions. First, it prevents a seesaw action of the sole as the runner's weight shifts from heel to toe, which seesaw action would reduce energy return. Second, the parallelogram enables the heel-pop (enhanced heel-lift) action needed for energy return. However, it turns out that both the curved-spring feature (the curved springs) of the version of FIGS. 1-3 and the version of FIGS. 4-6 accomplish both of these functions, in which case the second structure, namely a foot parallelogram, is extraneous. That is to say, the front and rear curved springs take the place of the front and rear links of a parallelogram. However, this pair of curved springs allows some seesaw deformation, but this is negligible and more than worth it because of the elimination the extra parallelogram structure. Even so, the disadvantage of the version of FIGS. 4-6 is that front curved spring 60 and rear curved spring 62 provide all the resistance of the spring system, and these are linear springs with linear force curves (unlike the version of FIGS. 1-3).

FIGS. 7, 8, and 9 depict schematic side views at heel strike, mid-stance compression, and toe-off of parallelogram heel-pop shoe 2 which is the third version of the first embodiment of the invention, namely the heel-pop energy return shoe. The basic structure features a shoe sole which comprises forward leaning foot parallelogram 4 under the foot and matching front parallelogram 6 under the toe. These parallelograms share a link, and this constrains their top links to compress together. Two designs for these parallelograms can be used and are shown. Copies of monolithic linkage 40 are shown separately at heel strike, full compression, and toe-off. These copies are immediately above the figures of the full shoe, and their elements are labeled separately because there are so many elements close together. The figure for hinged linkage 42 is shown only at heel strike just to demonstrate that all the hinges 34 can be conventional—that is, they comprise shafts and bearings for which the design and construction are obvious to one of ordinary skill in the art. However, the use of shafts and bearings entails the following shortcomings. The weight is increased, the vertical space needed increases the sole height, the construction is more complicated, and the cost is higher.

The design of monolithic linkage 40 is challenging because the pivots and the links are monolithically joined. The links are necked down near the pivot, and this necked-down section must bend in such a manner that it will not break after many duty cycles. This means that the requirement that link material be strong and rigid is compromised by the requirement that the pivot material must be very flexible. One solution taught in detail for the first time in the instant invention is to use fiberglass for the monolithic material, and to change the thickness to transform from the rigid link section to the flexible pivot section. Since none of the elements of monolithic linkage 40 are used as springs, it is also feasible to use thermoplastic polyurethanes or like materials which have considerable compliance and which can be injection molded. PEBAX 5533 and Pellethane are examples. The detailed shapes of these link-to-pivot connections are shown in the drawing for monolithic linkage 40.

First, let us look at hinged linkage 42 because it is easier to understand. Front parallelogram 6 comprises top toe link 19, front toe link 18, bottom toe link 17, and front link 28 (which is the shared link with foot parallelogram 4). All of these links are hingeably connected by hinges 34. Foot parallelogram 4 comprises rear link 27, top link 29, bottom link 30, and front link 28, which is the shared link with front parallelogram 6. Note that tension band 302 is one type of spring which can be used to resist the compression of front parallelogram 6, and it is only shown in this view. The force curve due to tension band 302 goes to zero approaching full compression, so an auxiliary linear spring (such as compression curly v-spring in the view of parallelogram heel-pop shoe 2 of FIG. 7) would have to be used to achieve the constant total force curve discussed for optimal springs in FIG. 12 and in FIG. 13. The preferred material for any tensioned band 302 herein is the continuous wavy composite without the viscoelastic layers—mentioned in the discussion of FIG. 27. Next, looking at monolithic linkage 40, rear mono link 9 connects to bottom mono link 12 via bottom rear mono pivot 16 which connects to front mono link 10 via bottom front mono pivot 15, which also connects to front mono link 10, which connects to top mono link 11 via top front mono pivot 14. Top mono link 11 connects to rear mono link 9 via top rear mono pivot 13—to complete the circuit. Front mono link 10 also acts as the rear link of front parallelogram 6; it connects to bottom toe link 17 via toe bottom rear mono pivot 25. Bottom toe link 17 connects to front toe link 18 via toe bottom front mono pivot 24 which also connects via toe top front mono pivot 22 to top toe link 19, which finally connects via toe top rear mono pivot 23 to front mono link 10—to complete the circuit for front parallelogram 6. Note that the bottom of front mono link 10 has a three-way connection. That is the reason that there are two pivots shown. Monolithic linkage 40 is not a perfect linkage like hinged linkage 42, but it is good enough, and it is much easier to mass produce.

With reference to FIGS. 7, 8, and 9, parallelogram heel-pop shoe 2 comprises monolithic linkage 40 which is described above and which is spring loaded; it further comprises 3^(rd) anti-toe-sink mechanism 8 which further comprises front parallelogram 6. Footplate 3 may be one and the same with top mono link 11, or it may be the bridge plate across the width of the shoe if foot parallelogram 4 is located only on the sides. Likewise is true for groundplate 5 and bottom mono link 12. One or more of diamond linkage tension springs 38 can be placed inside of foot parallelogram 4 in such a manner that these springs flatten completely at full sole compression, as shown in FIG. 8. That is, they are tilted backward slightly as shown in FIG. 7 so they can fully compress as in FIG. 8. These are optimal springs as explained in the discussions of FIG. 11, FIG. 12, and FIG. 21 (where they are referred to as tension curved springs 330, which is one example of a diamond linkage tension springs 38). Provided they permit footplate 3 to translate forward with respect to groundplate 5, any of the other optimal springs herein described can also be used, such as internal linkage mirrored arch spring 107 of FIG. 13 (especially in the monolithic version as described in FIG. 15), or such as the monolithic tensioned mirrored arch spring 200 of FIG. 18, tensioned band mirrored arch spring 292 of FIG. 20, or the two examples shown in FIG. 22.

As will be explained later in the discussion of FIG. 12 for optimized force curves and of figures herein for various kinds of optimized springs, these springs reduce the maximum impact force by achieving a force curve that has a constant force curve over the later range of compression. As will be discussed in detail later for FIG. 10, compression curly v-springs 37 meet this forward shifting requirement since they feature a floating hinge. Other springs such as kite end curved spring 144 of FIG. 16 or arrowhead curved spring 145 of FIG. 17 can also be used if they are configured with floating hinges as shown in FIG. 17. Any of these springs can be positioned in a particular location at a particular orientation with compressible positioner 39 as in FIGS. 7-9. These are firm enough to maintain a spring in position, but weak and compliant enough not to absorb much energy when compressed. Before leaving the discussion of the heel-pop shoes it is important to note that for a particular type of use the anti-heel-sink feature is not needed. That is to say when the impact force is always the same, the strength of the spring system can be chosen so that the sole always just barely fully compresses at that particular impact force. Then there is no need for the anti-toe sink feature. An example could be a walking shoe where the impact is constant. Another example could be a jogging shoe where the user jogs at pretty much the same speed all the time. This option is covered by the claims of the instant invention.

Mirrored arch springs 80 of FIG. 10 and the various refined versions in FIGS. 12-17 can also be used, provided the center tops and bottoms are slightly raised and rounded, in which case these springs can rotate forward in like manner to how diamond linkage tension spring 38 of FIGS. 7-9 rotates from being inclined rearward in FIG. 7 to being oriented with the top vertex being located directly above the bottom vertex in FIG. 8 at full compression. However, mirrored arch springs 80 have linear force curves as compared with the optimal force curves discussed later herein, and, hence, the advantage of impact reduction is not realized. The other springs discussed herein meet the requirement of optimal force curve in varying degrees as will be explained more fully later herein.

Regarding other more conventional types of springs, remember that footplate 3 is moving forward substantially with respect to groundplate 5. This means that conventional springs, such a helical or spiral springs, do not work. Actually, these could be used if either the bottom or top of the spring can slide along the adjacent surface, but that would be highly objectionable due to sliding friction. Torsion springs at the hinges would work, but those are far too weak in view of the fact that the sole must compress to a very small thickness, of the order of a quarter of an inch. All manner or curved springs and sinusoidal springs can act in tension between front para hinge 18 and its opposite hinged vertex in foot parallelogram 4, but these solutions are very weak and, even if they were strong, they would exert a very large compressive force on the link elements of foot parallelogram 4. The use of diamond linkage tension spring 36 or internal linkage mirrored arch spring 107 of FIG. 13 is far more optimal.

Note that foot parallelogram 4 may be preferentially located only at the perimeter sides of the sole. In this case footplate 3 comprises support elements on both sides and outside of the foot, and it comprises at its bottoms a minimally thin plate which extends across the center of the sole. In this way, the springs will act directly against this center plate adjacent to the runner's foot. This minimizes the strength and weight requirements for the side elements of foot parallelogram 4. The same can be done for groundplate 5. These variations of footplate 3 and groundplate 5 are not shown in detail, but are obvious to one of ordinary skill in the art. In this case, the various hinges of foot parallelogram 4 would also be preferentially located only at the sides of the sole. The 3rd anti-toe-sink mechanism 8 functions in almost exactly the same way as was the case in FIGS. 1-3, although its construction is slightly different. This can be seen in FIG. 9 where front parallelogram 6 remains compressed as foot parallelogram 6 opens up during heel-lift.

Note that it is possible to imagine applications in which the impact force of walking or running is fairly constant—e.g. for walking. In that case, a properly tuned shoe sole always fully compresses. The term properly tuned means that the spring system force is chosen or adjusted so that the shoe sole just barely fully compresses. In this case an anti-toe-sink mechanism is not needed. Even so, such heel-pop shoes without the anti-toe-sink mechanism are still novel and patentable since they still provide enhanced heel-lift. Also, note that it is easy to incorporate a spring under toe plate 7, but the main goal of the heel-pop inventions is to return virtually all of the foot impact energy into enhanced heel-lift. Any toe spring detracts from that goal. The reason for this design goal is that the runner's center of mass has been mostly accelerated upward and forward by the time this toe spring acts, in which case as toe spring contributes only negligibly to energy return.

The second embodiment of the invention is a class of novel springs, referred to herein as optimal springs in that their force curves are optimized. These can be complex springs or spring systems. The optimal spring class comprises variations on curved springs and arch springs. These variations are designed to optimize the force curve for footwear and for a number of other applications—where it is advantageous to minimize the maximum force (especially when there is an impact force) on the device structural elements and/or on the user of the device such as a runner. The optimization criterion is to maximize the amount of energy absorbed, namely the area under the force curve for a given maximum force point on that curve. If there are no geometric constraints on the size of the spring, then various conventional springs can be used to achieve force-curve optimized springs, or spring systems. However, the force-curve optimized springs in the instant invention achieve the minimum thickness at full compression of the entire spring, or complex spring. They also minimize friction losses by eliminating hinges or sliding friction elements. Finally, they minimize internal energy hysteresis loss by using fiberglass or another fiber reinforced composite which flexes or stretches sufficiently, such as the modified material of Pratt discussed elsewhere herein.

Arch springs comprise elemental curved springs such as front curved spring 60 in FIG. 4; these curved springs are loaded in such a manner that they fully flatten at full spring compression. Thus, these springs can flatten to an optimally small percentage of their uncompressed height. The fully compressed thickness value can easily be as small as a few percent, 5% e.g., of the uncompressed thickness. The ratio of uncompressed thickness to fully compressed thickness is referred to herein as the compression ratio. Thus, the compression ratio that corresponds to this 5% has a value of 20. These elemental springs are combined to construct the various types of arch springs and complex arch springs. FIG. 10 shows schematic side views of mirrored arch spring 80. Examples of possible configurations that can be built from the elemental curved spring include upper arch arm 84, mirrored arch spring 80, and curly v-spring 96, all of FIG. 10. All of these springs flatten to minimal fully compressed thicknesses. As such, they offer a big advantage over other conventional springs such as helical springs in applications such as shoe springs where there is a severe constraint on how thick their uncompressed sole thicknesses can practically be. In addition, they make possible far more versatility in spring systems. In more detail, the goal in a shoe is to minimize the sole thickness. Typically, with conventional springs in shoes, the fully compressed thickness is perhaps half the uncompressed thickness. With arch springs or complex springs based on arch springs, the fully compressed thickness can be ˜10% of the uncompressed thickness, e.g. This means that the sole thickness can be almost halved for a given desired spring deflection. Returning to FIG. 10, mirrored arch spring 80 comprises upper arch arm 84 which impinges lower arch arm 86 when compressed by load surfaces 90 from above and below. Arch vertex tethers 88 connect spring tips 92 at the ends of upper arch arm 84 and lower arch arm 86. An alternative vertex for upper arch arm 84 and lower arch arm 86 is joined vertex 94, in which case the two arms neck down and join in such a manner that the mirrored arch spring 80 can fully compress. Note that it is possible to modify and utilize mirrored arch spring 80 for use in the heel-pop shoes herein. Heel-pop shoes require that the top surface of the shoe sole, footplate 3 in FIG. 7 e.g., moves forward with respect to the bottom surface, groundplate 4 also in FIG. 7; call this the relative motion problem, which precludes the use of most conventional springs such as helical springs. However, mirrored arch spring 80 of FIG. 10 can be modified so that its top and bottom have a circular shape, in which case it can simply roll to accommodate said relative motion, provided the rolling distance is small. Mirrored arch spring 80 should be initially oriented (rolled slightly rearward) so that it is symmetrically loaded at full compression—meaning that the line, between the vertices where upper arch arm 84 is rotatably connected with lower arch arm 86, is horizontal at full sole compression. This is fortunate because such “rolling” mirrored arch springs are particularly easy to insert into a heel-pop soles where conventional springs do not work because of the relative forward motion of the footplate with respect to the groundplate.

Another advantage of arch springs is that it is possible to vary the thickness profile along the length of the arch arms so that the stress energy density over the entire flattened area of that arm is constant. This constitutes energy storage optimization. The third advantage relates to the fact that it is possible to adjust, and thereby optimize, the force curve of the arch arms. Note in FIG. 10 that mirrored arch spring 80 comprises four curved springs 97, each of which flattens to a straight plate at full compression. Herein, each curved spring is referred to simply as a curved spring. Also top curly arm 98 is simply one example of curved spring 97, as indicated in FIG. 10. Note that when several individual curved springs 97 are combined to construct a more elaborate spring, such as the mirrored arch spring of FIG. 10, the resultant force curve has the same shape as that of each curved spring 97. Another combination used herein is curly v-spring 96. Finally, mirrored arch spring 80 can be split down the middle (when viewed from the side) so that only half is used—when space is limited. This is referred to herein as a one-sided mirrored arch spring. It also happens that both the structure and the shape of each curved spring 97 can be varied so as to make the force curve more optimal. More importantly, the geometrical construction of each such elemental spring can be varied to achieve more optimal force curves, with reference to many of the figures that follow.

Let us return to the matter of the force-curve optimized spring and its criterion which is to maximize the amount of energy absorbed (namely the area under the force curve) for a given maximum impact force point on that curve. Another key advantage of the arch based springs herein is that they can easily be pre-loaded, for example to one-third of their eventual maximum force. FIG. 11 shows schematic side views of how both the elemental curved spring and mirrored arch springs can easily be loaded via pre-load tethers 106. Not pre-loaded curved spring 102 extends from its base, which is fixably attached to the lower one of load surfaces 90, to its upper end which will impinge the upper one of load surfaces 90 as it moves downward and leftward to begin to load not pre-loaded curved spring 102. At the chosen level of pre-load as shown by pre-loaded load surface 103, the upper one of load surfaces 90 is tethered by pre-load tethers 106. This prevents the upper one of load surfaces 90 from moving upward while it allows the top load surface 90 to move downward to further load pre-loaded curved spring 101.

In like manner, not pre-loaded mirrored arch spring 104 comprises four elemental not pre-loaded curved springs 102 configured as shown to form the mirrored arch spring type of the class of arch springs. Its top and bottom surfaces will impinge the upper and lower load surfaces to begin to be compressed. At the chosen level of pre-load as shown by pre-loaded load surface 103, upper and lower load surfaces 90 are tethered by pre-load tethers 106 to maintain pre-loaded mirrored arch spring 105 in the chosen state of pre-load. Various methods of maintaining the tips of the arch springs in intimate contact one to the other are described elsewhere herein. Next, it will be shown how the pre-load helps to optimize the force curve.

FIG. 12 shows force curves for two kinds of springs—a pre-loaded spring with a soft (regressive) force curve and a pre-loaded linear spring. Note that the area under each force curve is the energy absorbed by the spring. When the spring is pre-loaded, the required energy is stored at a lower value of the maximum force. In the example of the curve in FIG. 12 for the linear spring, there is a 25% lower reaction force with pre-load. In the example of the curve for the non-linear soft spring, there is a 40% lower reaction force with pre-load as compared with a linear spring without pre-load, again for the same energy stored. It turns out that it is possible to vary the shape, the geometrical structure, and the thickness taper along the spring arm length so as to approach or sometimes even achieve the optimal constant force curve. In the case shown in FIG. 12, the pre-load starts at about one-third of the maximum force value. It then rapidly increases for about one third of the total deflection; it then asymptotically approaches the constant maximum force value. Thus, the first part of the method to achieve a desired optimized force curve with a minimum value for the maximum force on the curve is to pre-load it. The second part is to vary the spring structure and shape so as to achieve a softer, more constant force curve. The third part of the method will be explained later. It raises the need to determine the optimal energy to be stored in the shoe sole, and it points out that Tables 1, 2, and 3 can be used to realize this optimal sole energy. Another key insight is that just because a force curve is constant does not mean that foot impact energy is still being absorbed for that final portion of sole compression. In fact, for the various linkage-spread and arch tensioned or compressed springs of the instant invention, a reduced amount of impact energy is stored, over what would be miscalculated by simply using the area under the constant force curve as a function of compression distance. The various auxiliary springs in the designs of the instant invention make sure that the optimal amount of impact energy is still being absorbed and store for energy return as full spring compression is reached.

With reference to Table 1, for the size regime of shoe soles (with spring heights of one-half to three inches), the mirrored arch springs herein made of fiberglass are 10.5 times stronger than carbon fiber springs and sixteen times stronger than arch springs made of the injection moldable materials such as the thermoplastic elastomer PEBAXX 5533 mentioned in the prior art of the summary of the instant invention. A non-linear finite element analysis was required to come to this scientific conclusion. Notably, this result is not obvious and it has not been even mentioned in the prior art based on an extensive search by the instant inventor. Thus, fiberglass is claimed herein as the material of choice for the arch and curved spring based springs used in both heel-pop shoes and in conventional shoes. Furthermore, the instant inventor did not find any prior art, which discloses the basic spring structure of two facing hemispheres hingeably connected (in either circular or cylindrical geometries), that even mentions fiberglass as the material of choice or which teaches the scientific data necessary to prove that fiberglass is by far the superior material in shoe applications. There might have been cases where a blanket statement is made that “any material could be used for any element,” but this teaches nothing. As such, it would not hold up in litigation. Rather, this prior art is totally focused on the use of injection moldable plastics such as thermoplastic elastomer PEBAXX 5533. Also, these prior art springs do not compress to the optimally minimum thickness of the arch springs of the instant invention because the sides of the hemispheric sides are so bulky—because the material is so weak for bending applications.

The spring strength results used for the Table 1 and later for Tables 2 and 3, use the following material specifications. The ANSYS FEA model used the mechanical properties from “GC-70-UL: UNIDIRECTIONAL FIBERGLASS LAMINATE” Eglass available from Gordon Composites. (http://www.gordoncomposites.com/products/TDS/GC-70-UL.pdf) Of course, the modulus of Sglass is approximately 20% stronger than for Eglass, and the strength is approximately 30% stronger. This indicates that for the fiberglass made arch-based springs herein, their strength could be more than twenty times stronger than the PEBAX 5533 made springs of the prior art mentioned in the summary of the instant invention. This is very significant! The reason that fiberglass shoe sole springs are so much stronger than carbon fiber composites is that the strain limits are higher by a factor of four (than those for carbon fiber laminates or titanium, e.g.), and this increased strain limit is the critical parameter in this size regime.

Curly v-spring 96 in FIG. 10 was used for the non-linear finite element analysis. This model was used to calculate the values in Table 1. The first section of the table, for the curly spring, reports the following parameters. Each of the two arms, top curly arm 98 and bottom curly arm 100, is a quarter of a circle with a particular radius. The deflection, d, equals twice the radius minus twice the arm thickness, t. The force f is at 80% compression. These results assume a spring width of one inch. At full compression the arms would be fully flattened. Note that the thickness values are only five percent of the radius values, or 2.5 percent of the deflection values. Thus, the first significant advantage for fiberglass composite is that the fully compressed thickness is only 2.5% of the deflection which corresponds to a compression ratio of 40. This demonstrates the first advantage of complex springs based on elemental curved springs and made of fiberglass. The second significant advantage has to do with the relative spring load force values for the four materials. The spring load force for fiberglass composite is by far the highest. It is 10.5 times higher than the value for carbon fiber composite; it is 9.3 times higher than value for titanium; and it is 16 times higher than the value for PEBAX 5533. Thus, fiberglass is by far the preferred material for these springs. That is, the second significant advantage is that fiberglass is much stronger. Also, taking into account the differences in density, the spring weight for these fiberglass springs is 12.3 times lighter than for carbon fiber springs, and it is 8.2 times lighter than for PEBAX 5533. Thus, the third significant advantage is that fiberglass is much lighter, because the spring widths are less. The advantage of injection moldable materials is that they are cheaper and easier to make, but fiberglass springs can be mass produced as well.

Table 1 shows a very interesting feature which leads to another part of the method to optimize force curves, certainly for shoe applications and probably for other applications. Close inspection reveals that the ratio of force f to deflection d and the ratio of arm thickness to deflection are constant over the entire range of deflection shown, for each material. This is not unexpected because top curly arm 98 behaves like a cantilever or a diving board which starts with the shape of a quarter circle and bends (compresses) to flatten. Thus, the load force is proportional to the thickness cubed over the length cubed, so these two load force ratios would be expected to remain constant. Likewise, the ratio of d to t also remains constant.

However, looking at the second part of table 1 for the curved spring, which corresponds to the top or bottom half of the curly v-spring, note that for a given deflection d, say 2″, the force, f is twice that for the curly v-spring (184 lbs as compared with 92 lbs). Likewise is true for the thickness, t (0.096″ as compared with 0.048″). Thus, the curved spring arm is thicker than the curly spring arm, and the achievable force is doubled. That is why the heel-pop shoe spring systems (using curved springs) are twice as strong and, hence, twice as light as springs used for convention shoes (see FIG. 24) which use mirrored arch springs (which are equivalent to curly v-springs for the purposes of this argument). Here is a conclusion which may seem surprising. Note that for these curly v-springs, increasing the deflection by a factor of ten increases the load force by a ten of ten. However, ten times as many springs can be fit into the same area (footprint) for the smaller deflection value. This means that the total force per area achievable is constant over the entire range of deflections for all spring heights (˜d). This is the important insight. Assuming that the force curve is linear, the impact energy stored by the spring at full compression is equal to the maximum force times one-half the deflection. Thus, the possible energy that can be absorbed is linearly proportional to the deflection. Next, how is this insight relevant to the question of optimizing a spring for an application such as running?

The impact energy of running is absorbed by two elements: the leg and the shoe sole. In a manner similar to two springs in series, impact energy is stored via resisted deflection of both the leg and the sole. For springs in series, when one element is very rigid, more impact energy is absorbed in the other element. If the sole is very rigid, the leg must absorb almost all the impact energy, mostly in the knees. Thus, the more deflection there is in the sole, the more energy is stored in the sole and the less work the leg has to do to absorb the energy. However, there is a limit to how thick the sole can be because the combined knee and ankle action to thrust the runner back into the air makes the determination of optimal coupling quite complicated. Even so, it is likely that the energy cost of running can be significantly reduced if the sole deflection is made as large as is practically possible, in which case the runner would run with less knee bend, which in turn reduces the energy absorbed in the quadriceps muscles. In addition, by optimizing the force curve as was discussed for FIG. 12, the maximum impact force can still be less than is the case with conventional prior art shoes with springs which are linear and not pre-loaded and with springs which typically deflect only about a quarter of an inch. This consideration, to maximize the sole thickness and, hence, the energy stored in the sole, is the third criterion of the method for optimal springs—to achieve a desired optimized force curve with a minimum value for the maximum force on the curve, discussed earlier for FIG. 12.

With these considerations in mind, it makes sense to determine the impact energy of running, and then to vary the sole deflection to determine the maximum energy that can be stored in the sole without compromising the leg/ankle action and the timing of the coupling action of running. With this optimal sole energy determined, it is then a simple exercise to use Table 1 to calculate the optimal deflection using the equation, spring work equals one-half the deflection squared—for a linear spring. If the spring force curve is non-linear, the force curve can be easily determined and used to achieve the same result. In summary, another part of the method to optimize the force-curve discussed for FIG. 12 is the following. One must determine the optimal energy to be stored in the sole spring, and one must use a table such as Table1 to then determine the optimal deflection to realize this sole energy—in view of the fact that the stored energy is linearly dependent on this deflection for the optimal springs of the instant invention.

FIG. 13 shows schematic side views of internal linkage mirrored arch spring 107. This spring is designed to be an optimal spring with a force curve which starts linear and which then bends over to be constant. First, let us look as FIG. 19 for tensioned linkage spring configurations, and specifically at tensioned diamond spring 282. Vertical loads (shown by force load arrow 258) compress vertical vertices 256 together. This motion is resisted by generic tension spring 250 via side vertices 254. As 4-sided linkage 252 is compressed, the vertical force needed to pull apart tension spring 250 first increases and then reduces to zero. That is, at full compression the links are horizontal and, hence, provide zero vertical force. The design of FIG. 13 is actually based on compressed diamond spring 286 of FIG. 19 where, as 4-sided linkage 252 is compressed by vertical loads shown by force load arrow 258, this motion is resisted by generic compression spring 250, which compresses against fixed anchor 272. Again, the vertical force needed to push apart generic compression spring 274 first increases and then reduces to zero. Looking again at FIG. 13 for internal linkage mirrored arch spring 107, let us see how the same force curve is achieved even though the configuration is somewhat different.

FIG. 13 with schematic side views shows the favorite enhanced optimal spring herein, namely internal linkage mirrored arch spring 107 which comprises the following elements. Load surfaces 90 compress monolithic mirrored arc 108. Mirrored spreader linkage 115 comprises (on top and bottom) center links 113 which are pivotally connected on both sides via corner hinges 120 to mostly vertical links 114, which are pivotally connected on both sides to impinger links 112 via impinger hinges 119. Inside linkage partial springs 117 are located between upper and lower, center links 113, and they are located spaced away from each other to provide a restoring force to keep center links 113 horizontal during compression. Likewise is true for outside linkage partial springs 116. The reason for the need for this restoring force is that the top and bottom halves of mirrored spreader linkage 115 are inherently unstable, meaning that this half linkage could possibly shift sideways so that one adjacent corner hinge would be higher than the other—if the loading by outside linkage partial spring 116 were at the center of center links 113.

Now, for the interesting insight remembering compressed diamond spring 286 of FIG. 19, monolithic mirrored arch 108 acts as generic compression spring 274 of FIG. 19. That is, it resists the outward expansion of mirrored spreader linkage 115 as if it were a compression spring. And, instead of pushing in compression against fixed anchors 272 of FIG. 19, they push against the monolithic pivots of monolithic mirrored arches 108, which are shown in more detail in FIG. 15 as monolithic arch hinges 187. Thus, all of the comments made, for the how compressed diamond spring 286 of FIG. 19 is an optimal spring with an optimal force curve, apply for internal linkage mirrored arch spring 107, which is even more optimizable by virtue of (1) the action of outside linkage partial springs 116 which control and moderate the initial spreading of monolithic mirrored arch 108 by mirrored spreader linkage 115, and by virtue of (2) the action of inside linkage partial springs 117 which prevent the force curve from going to zero at full compression. That is, the force curve starts linear and then becomes constant—qualifying internal linkage mirrored arch spring 107 as a fully optimal spring. Compressed internal linkage mirrored arch spring 109 shows the behavior during compression. Note that all elements flatten at full compression to maximize the compression ratio. Impinger hinges 119 and corner hinges 120 can be conventional cylindrical hinges with shafts and bearings, but preferentially they are necked-down living hinges as shown below in FIG. 15. Note that a simple four-sided diamond shaped linkage does not work because that flattened length is less than the flattened length of upper arch 110. Thus, the extra links (center link 113 and impinger link 112) are needed to fully spread upper arch 110.

FIG. 14 shows schematic side views for various configurations of the internal linkage curved spring. Note that 1st double link-spread curved spring 122 is an example of linkage-spread curved spring 121, and it comprises double linkage 131 which comprises two double links 125 connected by double hinge 126. Double linkage 131 hingeably connects on either side via spring hinges 124 to curved spring 127, which is inclined to the left from vertical. Top adjust spring 132 is located between double hinge 126 and its adjacent load surface 90. Adjust spring 133 is located so that it is loaded only by load surfaces 90. The goal of this design is for double linkage 131 to spread and straighten curved spring 127 so that the force curve bends over at a partial compression. Top adjust spring 132, and adjust spring 133 are optional, but serve to achieve a more optimal force curve. Top adjust spring 132 controls the onset of the loading of double hinge 126 by load surface 90. Adjust spring 133 serves to maintain the total force curve approximately constant as the force curve just due to the linkage spreading of curved spring 127 would begin to go to zero without adjust spring 133. As the top load surface 90 compresses, eventually double hinge 126 is higher than the top spring hinge 124, at which time curved spring 127 is only loaded in spreading so that the force curve will bend over and eventually go to zero (without adjust spring 133). The onset of the pure spreading loading is shown by the figure for compressed 1st double link-spread curved spring 123.

An example of another version of linkage-spread curved spring 121 is 2nd double link-spread curved spring 135. Here the lengths and the angles of the component links of double linkage 131 have been changed so that double hinge 126 impinges the top load surface 90 earlier during the spring compression. This causes the force curve to bend over sooner. The summed length of the two double links 125 must equal the length of curved spring 127 so that all elements can fully flatten at full compression. Two representations of 2nd double link-spread curved spring 135 are shown, the first at the beginning of compression and the second when double hinge 126 impinges load surface 90. This second representation is compressed 2nd double link-spread curved spring 136. In this double-link version and in the next triple-link versions, top adjust spring 132 and adjust spring 133 are not shown, but they can well be used to better refine the force curve. Tip path 130 traces the path of the tip of curved spring 127 as it is compressed to flatten.

The next two figure views show two versions of with a linkage comprising three links. Again, the lengths and angle of the component links are changed to alter when the force curve bends over, and two levels of compression are shown. 1st triple link-spread curved spring 137 comprises three tri links 128 connected by two tri hinges 129. It also spreads curved spring 127 during compression. Optional top adjust spring 132 and adjust spring 133 are not shown, but they can also be used to better refine the force curve. Compressed 1st triple link-spread curved spring 138 indicates the compression where the top tri hinge 129 impinges the top load surface 90. Another version is shown with 2nd triple-link spread curved spring 139 and compressed 2nd triple-link spread curved spring 140, where the top tri hinge 129 impinges the top load surface 90 earlier during compression. All versions here can be combined in mirrored versions about the center vertical line to make an arched configuration, which in turn can be mirrored about the horizontal center line to make a mirrored arch configuration.

FIG. 15 shows a schematic cut-out side view of cut-out monolithic mirrored spreader linkage 183 which portrays in detail a monolithic, necked-down living hinge version of mirrored spreader linkage 115 of FIG. 13. The full links are not shown to better view the pivot sections, but the center, link sections are indicated by the wavy lines. This is referred to as a cut-out herein. Cut-out monolithic mirrored spreader linkage 183 comprises monolithic center links 185 which connect via monolithic corner hinges 182 to monolithic mostly vertical links 186, which connect via monolithic impinger hinges 181 to monolithic impinger links 184 which impinge monolithic arch hinges 187, which connect upper arch 110 with lower arch 111 (see FIG. 13). As stated before, the preferred materials, for linkages like cut-out monolithic mirrored spreader linkage 183, are TPUs of appropriate hardness such as PEBAX or Pellethane, because these materials can be injection molded, or like materials. Also, the preferred and by far the strongest material for the curved springs herein is fiberglass.

FIG. 16 shows schematic side views of kite-end curved spring 144 at various levels of compression including first level compressed kite end curved spring 146, second level compressed kite end curved spring 147, and fully compressed kite end curved spring 148. Kite end curved spring 144 is compressed between load surfaces 90 in such a way that the top load surface 90 is free to move horizontally with respect to the bottom load surface 90. Solid initial section 152 is fixably attached to the lower load surface 90 at its beginning (base). It forms a monolithic structure with kite end section 149 which comprises the following: inner arch 153, outer arch 154, kite end section 149, spring end 151, and optional vertices tether 150. These two arches form a mirrored arch to be compressed. Optional vertices tether 150 is shown only in the uncompressed view in view of space limitations. Its first purpose is to prevent inner arch 153 and outer arch 154 from moving apart during the initial part of compression. Its second purpose is to pre-load kite-end section 149.

The idea behind kite-end curved spring 144 is that the character of the loading of kite-end section 149 changes during compression. Initially, it is oriented diagonally with respect to the upper load surface 90, during which time it receives primarily a bending load via spring end 151. The view of first level compressed kite-end curved spring 146 then shows that kite-end curved spring 144 has rotated counterclockwise so that the upper load surface 90 is beginning to directly load kite-end section 149, at which time the loading becomes primarily compressive rather than bending. Just at this level of compression (approximately 60% in this example in first level compressed kite-end curved spring 146), solid initial section 152 has been approximately flattened. Up until this level of deflection, the initial force curve force curve of kite-end curved spring 144 has been primarily due to the flattening of solid initial section 152. Now however, the force curve for the remaining 40% compression of kite-end curved spring 144 can be reduced in slope because it is due to the compression of kite-end section 149. In the first part of this compression of kite-end section 149, it is obliquely loaded so it is stiffer. This can be seen in the third view—of second level compressed kite-end curved spring 147. As full compression is achieved, kite-end section 149 is loaded more directly so that the force curve will soften. This can be seen in the fourth view—of fully compressed kite-end curved spring 148. With these detailed considerations in mind, it is apparent that the force curve of kite-end curved spring 144 can be engineered to bend over and to become significantly softer (more digressive). Thus, the goal to optimize the force curve by minimizing the maximum impact force has been achieved. Of course, spring end 151 could as well be hingeably connected to the top load surface 90, or it could be rollingly connected as has been previously detailed herein. Another option is to use optional vertices tether 150 to pre-load kite-end section 149.

FIG. 17 shows schematic side views of configurations for arrowhead, kite-end and double-link spread curved springs. First it shows a schematic side view of mirrored kite-end curved spring 169 uncompressed. The combination of four ones of kite-end curved spring 144 (from FIG. 16) results in the formation of mirrored kite-end curved spring 169. This combination forms a mirrored arch spring similar to mirrored arch spring 80 of FIG. 10. Accordingly, the elements of mirrored kite-end curved spring 169 comprise the same elements as those of kite-end curved spring 144. Thus, mirrored kite-end curved spring 169 comprises upper kite end arch 172 and lower kite end arch 173, each of which further comprise solid arch center section 170 and end kite section 171.

FIG. 17 also shows schematic side views of arrowhead curved spring 145. This demonstrates yet another approach to attain a more optimal force curve by utilizing a structure at the end of a curved spring for which the nature of the loading changes as the end rotates during compression. Arrowhead curved spring 145 comprises solid initial section 152 which is rigidly attached to the lower load surface 90 at its base and which is monolithically attached to arrow rigid end 158. Inner arrow arm 156 and outer arrow arm 157 are fixably attached to arrow rigid end 158, and these are leaf springs. Spring end 151 forms the end of arrow rigid end 158, and it impinges the top load surface 90. Thus, arrowhead end section 159 comprises inner arrow arm 156, outer arrow arm 157, arrow rigid end 158, and spring end 151. The view of mostly compressed arrowhead curved spring 159 shows that spring end 151 initially impinges load surface 90. However, eventually during compression arrowhead end section 159 rotates counterclockwise so that the tips of outer arrow arm 157 and inner arrow arm 156 now impinge the upper and lower load surfaces 90. At full compression the spring action of solid initial section 152 is acting in series with the spring actions of inner arrow arm 156 and outer arrow arm 157. Since the stiffness of in-series springs add reciprocally, this means that the sum force of these two spring actions is less than the force of just solid initial section 152. Hence, the force curve has bent over, and it more optimal as defined herein.

Kite-end v-spring 165 behaves similarly to curly v-spring 96 of FIG. 10 in the sense that is has floating hinges, which ensures that the top load surface 90 is free to translate to the left with respect to the bottom load surface 90—as indicated by top load surface arrow 168. And, the force curve is similar to that of kite end curved spring 144. FIG. 17 also shows a schematic side view of kite-end v-spring 165 which comprises top kite-end curved spring 162 and bottom kite-end curved spring 164 which are joined by kite-end v-spring vertex 166. Likewise, mirrored linkage-spread curved spring 163 is similar to curly v-spring 96, but the force curve is similar to that of linkage-spread curved spring 121 of FIG. 14—of which it is composed with two mirrored parts. Again, these force curves are more optimal (constant force) than the linear force curve of curly v-spring 96.

FIG. 18 shows compressed and uncompressed schematic side views of monolithic tensioned mirrored arch spring 200, which comprises the following elements. Inner side-loaded arch spring 204 is located inside of and pulls on outer top-loaded arch spring 206 via inter-arch section 208. These three elements form a continuous monolithic structure, and they are interconnected via necked-down living hinges. Also, the bottom half of this continuous monolithic structure is the mirrored image of the top half, although inner tension-loaded curly v-spring 220 is substituted for the inner tension element in the figure to show an alternative version. Outer top-loaded arch spring 206 comprises extended flat section 224 and outer-tip sections 210. The curved sections of inner side-loaded arch spring 204 and outer top-loaded arch spring 206 comprise sections that are quarter circles in shape approximately. The extension of extended flat section 224 permits these inner and outer arch elements to both fully flatten without interference one to the other. Although the curve shapes do not necessarily need to be quarter circles, this is a convenient method to ensure the necessary full flattening. The other provision, to ensure full flattening, is outer-tip spacer 218—as can be seen in the view of compressed monolithic tensioned mirrored arch spring 202. Note that the height of outer-tip spacer 218 is exaggerated for easy viewing, but it will be minimized so that all arch elements only just touch along their lengths at full compression. Outer clamps 216 clamp together the mirrored outer-tip sections 210 to outer-tip spacers 218, and inner clamps 214 clamp together mirrored inner-tip sections 212. To show another possibility for the inner tension element, inner tension-loaded curly v-spring 220 is shown instead on the bottom half of the structure, and it also fully flattens at full compression. Its mirrored halves are connected by inter curly-v tip section 222. Necked-down living hinges are depicted for inter curly-v tip sections 222, outer-tip sections 210, and inner-tip sections 212.

FIG. 20 shows another design where mirrored arch springs incorporate a tension spring element, in this case a stretchable band which in the prior art was made of a TPU-like material—which, however, has energy hysteresis losses of 20% to 50%. However, there are two distinct advantages of monolithic tensioned mirrored arch spring 200 of FIG. 18 over the design of FIG. 20: namely that the tension spring element, either inner side-loaded arch spring 204 or inner tension-loaded curly v-spring 220, can be made of fiberglass which has minimal energy hysteresis loss (˜1%), and the connection between the tension spring element can thus be made monolithic—since outer top-loaded arch spring 206 is much preferably made of fiberglass which is an order of magnitude stronger than TPU-like materials. However, with reference to the discussion in the prior art for Pratt, if it is possible to make the tension bands of a continuous wavy composite without the viscoelastic layers, then that would be more competitive. That option is claimed in the instant invention. Note also that said tension spring element serves to resist the compression of the outer top-loaded arch springs 206, so the combined spring action is stronger. However, as the whole spring assembly compresses, the action of the tension spring element becomes more aligned with the action of outer top-loaded arch spring 206 so that the vertical component of these opposing forces (which is directly opposing the compression between the opposing load surfaces 90) decreases and eventually goes to zero. Thus, the total force curve decreases, but note that it does not go to zero because the bending force of outer top-loaded arch spring 206 is still opposing compression. Thus, if the strength of the inner and outer arches are roughly the same, the total spring rate (the total force curve slope) starts at twice the value for just the outer arch spring, and then decreases to the value just due to the outer arch element. The conclusion is that the total force curve can be “half-optimal” because it cannot become horizontal. Moreover, this is not the case for the linkage spread curved springs designs of FIGS. 13, 14, 15, 19, 21, 22, 23 and 27 herein, which are completely optimal because the “total” force due to the linkage spread arch springs (or curved spring for FIG. 27) does go to zero, so that an auxiliary spring can be used to make the complete total force curve go constant when the auxiliary spring is included in the spring system. This is because there is no contribution to the force curve from the links, which do not bend.

The discussion of FIG. 19 pertains to goal of optimal springs which can fully minimize the maximum impact force point of running. These optimal springs are the second embodiment of the invention. FIG. 19 shows schematic side views of various configurations, called herein torque-lift configurations for optimal springs, in which a tension element is used to resist compression of a linkage in such a manner that the force curve for the spring-tensioned linkage assembly is optimal as defined by the criterion that the force curve starts linear and then bends over to stay essentially constant, although it may continue to increase with a lower slope. In tensioned diamond spring 282, vertical loads (shown by force load arrow 258) compress vertical vertices 256 together. This motion is resisted by generic tension spring 250 via side vertices 254. As 4-sided linkage 252 is compressed, the vertical force needed to pull apart tension spring 250 first increases and then reduces to zero. That is, at full compression the links are horizontal and, hence, provide zero vertical force. Compressed diamond spring 286 comprises 4-sided linkage 252 which is compressed by vertical loads shown by force load arrow 258. This motion is resisted by generic compression spring 250, which compresses against fixed anchor 272. Again, the vertical force needed to push apart generic compression spring 274 first increases and then reduces to zero. Now consider spring systems based not on linkages, but on mirrored arches—to explain why these are “half-optimal.” Tensioned mirrored arch spring 284 is loaded by load surfaces 90; it comprises outer upper arch spring 268 which is pivotally connected to its mirror image, outer lower arch spring 270, via pivot connections, 260. Likewise, inner upper arch spring 264 is pivotally connected to inner lower arch spring 266 via pivot connections, 260, which connect these inner and outer mirrored arches together via cords 262. By virtue of these connections, the inner mirrored arch springs resist the outward motion of the pivot connections 260 connecting outer upper arch spring 268 with outer lower arch spring 270. This increases the force needed to compress the whole spring assembly over the vertical compression force exerted just by the outer mirrored arch spring. In effect, the total spring stiffness is increased, and approximately doubled. Cords 262 exert only a horizontal tension force, which goes to zero as the inner arch mirrored spring approaches full flattening. This means that the contribution of the inner mirrored arch spring goes to zero, so the slope of the total vertical spring force goes to one-half of its initial value. This makes tensioned mirrored arch spring 284 “half-way optimal.” This is not as good as the linkage-spread curved spring systems herein which are fully optimal since their force curves approach a constant value, but it is still an improvement over a spring with a linear force curve. Note that care must be taken to ensure that inner upper arch spring 264 and inner lower arch spring 266 are loaded only horizontally via cords 262. If these inner arches are loaded vertically by impingement of their center sections with the outer arches, the slope of the force curve will increase to its initial value, or by approximately a factor of two, and the spring is no longer even “half-optimal.” Another problem with this design as shown is that the lengths of the inner arches are smaller than the lengths of the outer arches, which prevents the outer arches from fully compressing.

Compressed separated mirrored arch spring 288 solves the problem of fully flattening by separating the outer arches. It is very similar to tensioned mirrored arch spring 284. It comprises left half outer arch spring 278 and right half outer arch spring 280 which also have pivot connections 260 at their centers, and which also connect via cords 262 to the inner mirrored arches, namely inner upper arch spring 264 and inner lower arch spring 266. Note however that left half outer arch spring 278 and right half outer arch spring 280 are now connected by cords 262. The vertical forces are exerted by slotted spacers 276 as indicated by force load arrows 258. Interference between cords 262 and slotted spacer 276 is prevented by virtue of longitudinally oriented slots in slotted spacer 276 which permit passage of cords 262. With these provisions, separated mirrored arch spring can fully compress and flatten. It also has a “half optimal” force curve.

FIG. 20 shows schematic side views of tensioned band mirrored arch spring 292. Here the tension element is tension band 302 which loads the mirrored arch elements which are shown with rounded tip curved arm 296 on the left side and as necked-down tip curved arm 298 on the right side. This is just to show two options for the pivot at the tips of these mirrored arch elements. It is important that these tips can rotate ninety degrees without putting undue stress on the curved arm. During compression, rounded tip curved arms 296 on the left side and necked-down tip curved arms 298 on the right side, impinge their mirrored image vertically through the ends of tension band 302. To further prevent tension band 302 from sliding out between these impinging tips, band end loop 306 encloses hollow rectangular band retainer pin 300 so that this assembly cannot squeeze down to pull through the space between the mirrored images of impinging tips of rounded tip curved arms 296 on the left side and necked-down tip curved arm on the right side. This appears to be the easiest failsafe method for attachment so that tension band 302 cannot squeeze and pull through. This method is both novel and easy to fabricate. After cinching the assembly tightly together with stitched cord 306, hollow rectangular band retainer pin 300 is simply inserted from the side through band end loops 304. The view of compressed tensioned band mirrored arch spring 294 shows the spring assembly at full compression by load surfaces 90. Note that stitched cord 306 must be easy foldable. Band loops are easy to make of injection moldable material.

The view of pre-load stitching configuration 312 indicates how to fabricate stitched cord 306. Vertical arm pre-load holes 308 are made across the center top of rounded tip curved arms 296 (or of necked-down tip curved arms 298 if that version is used), and likewise for band pre-load holes 310 in tension band 302. Then stitched cord 306 is threaded going across the width of tensioned band mirrored arch spring 292 at its longitudinal center. Provided that a suitable material can be found for tension band 302 the design of FIG. 22 appears to be a suitable solution for the tension element attachment. Thermoplastic polyurethanes appear be strong enough and to stretch the necessary 60%, but they appear to have significant hysteresis losses of ˜20-50%. If energy return of the springs does not need to optimized, then these TPU's could be used in the design of FIG. 20. If optimal energy return is needed, then the design of FIG. 18 is preferable since it uses bending fiberglass curved arms for the tension element, which are 98% to 99% energy efficient. That is, their hysteresis loss is only 1-2%. Lucas in U.S. Pat. No. 7,401,419 of Jul. 22, 2008 show figures for hysteresis loss which appear to indicate a hysteresis loss of 20-30% for TPUs. Other data in the literature indicate hysteresis losses of 40% for these materials. Note that technique of pre-load stitching configuration 312 can be used anytime that a spring system needs to be pre-loaded or held in place. For example, refer to FIG. 11, FIG. 13, FIG. 18, or FIGS. 21-23 herein.

Another possible candidate for the tension element is a wavy shaped length element, presumably made of fiberglass. However, the force curve of such a serpentine (e.g., sine wave) element is inherently hard. This means the amplitude of the undulations would have to be high which would compromise the minimum height. Also, the maximum strength of curved elements decreases dramatically as the effective radius curvature decreases. This is shown in Table 1. For this reason the number of cycles (undulations) of the tension element is minimized in the instant invention. Finally, hot off the presses, the other option for tension band 302 is the continuous wave composite (CWC) of Pratt in U.S. Pat. No. 7,906,191 of March 15. This is discussed in detail in the prior art section of the summary of the invention herein. It can be made of fiberglass or carbon fiber, or any other fiber composite, for that matter. And, it should be made without the viscoelastic layers for optimal energy return. Moreover, here is one way to make it. Start with a length of CWC at the center of tension band 302, so to speak. Run this length to and around a first of two hollow rectangular band retainer pins 300, then back along its first section to and around the other (retainer pin), and then back to the original band end. This will now look like tension band 302 except that there the two center sections of the length are not glued together. Simply glue them together, or apply a heat treatment to melt the contact surfaces together. Since the upper and lower sections are now glued along the entire length, tension band 302 should not pull apart. A clamp where the ends join could “seal the deal.”

FIG. 21 shows schematic side views of two tensioned linkage configurations. Tensioned linkage spring 320 uses bending fiberglass curved springs as the tension elements, and band tensioned linkage spring 340 uses tension band 302. Tensioned linkage spring 320 comprises four quad links 322 which are pivotally interconnected by vertical hinges 323 and horizontal hinges 324 to form a diamond shaped linkage. Load surfaces 90 load vertical hinges 323. The tension element is comprised of tension curved springs 330 symmetrically arranged on four sides, which comprise initially vertically oriented tension spring tips 332 which interconnect via tip cords 326. At the other ends at the center of the arrangement, tension curved springs 330 connect to horizontal hinges 324 via hinge cords 328, which are clamped to tension curved springs 330 by tension clamps 334. Hinge cords 328 loop around horizontal hinges 324 to withstand the tension force. This looping is easily done if horizontal hinges 324 use a shaft—in which case one or more longitudinal slots are cut across the width of quad links 322. The loops of hinge cords 328 are then pushed through these slots so that said shafts can be pushed through said loops to achieve the tension connection in a manner obvious to one of ordinary skill in the art. The view of compressed tensioned linkage spring 321 shows how tension curved springs 330 are pulled to straighten during compression. This design is a fully optimal spring as has been defined herein several times, provided auxiliary springs are used to prevent the total force curve from going to zero as full compression is approached. See for example FIG. 7. Note that these auxiliary springs are of partial height of the deflection distance, and they need to be loaded directly by the load surfaces. Also, note that tension curved spring 330 was used as an example in this figure. Tensioned linkage spring 320 was the example used for diamond linkage tension spring 38 in FIG. 7, but many of the other optimal springs herein can be used as well, preferentially the ones of monolithic construction.

Also shown in FIG. 21 is band tensioned linkage spring 340. It uses the same four-sided linkage as tensioned linkage spring 320, but instead it uses tension band 302 for the tension element. The view of compressed band tensioned linkage spring 342 shows the compressed state. The explanation just given for tensioned linkage spring 320 explains the connections and function for band tensioned linkage spring 340. The caveats of hysteresis energy loss given for FIG. 20 for tension band 302 also apply here when it is made of TPU-line material, but it might be made of a variation of the wavy fiber material of Pratt discussed above.

FIG. 22 shows schematic side views of monolithic tensioned linkage configurations. These are similar to the designs of FIG. 21 except that the connections of the various elements are monolithic, utilizing necked-down living hinges. Monolithic tensioned linkage spring 350 comprises a four-sided, diamond shaped linkage comprising monolithic quad links 354 connected by monolithic vertical necked-down vertices 356 and by monolithic horizontal necked-down vertices 358. The monolithic construction continues with the connection of horizontal necked-down vertices 358 to side vertex connection sections 370 which divide in a merged sense to form monolithic tension curved springs 366, which connect to their mirrored images via monolithic tip connection sections 368. Optional elements used to reinforce the side connections comprise first necked restraints 364, monolithic loops 360, and retainer pins 362. Monolithic loops 360 are part of the continuous link/spring structure. Retainer pins 362 are inserted from the sides through these loops, and they serve, in combination with first necked restraints 364, to withstand the considerable compressive force exerted on monolithic horizontal necked-down vertices 358 by the action of monolithic tension curved springs 366. Since the monolithic structure has to serve as a spring element as well as a link element, fiberglass is the preferred material. This also applies to the necked-down living hinge elements. The view of compressed monolithic tensioned linkage spring 352 shows this design in compression by load surfaces 90.

Monolithic tensioned linkage spring 350 is the second most preferred tensioned optimal spring in the instant invention because it can be used to achieve a completely optimal spring with a completely optimal force curve. It features high energy efficiency (99%) of its spring element, monolithic tension curved spring 366, and it can be mass produced as an insertable spring in any shoe design, including the heel-pop designs of FIGS. 1-9 provided it is tilted backwards before compression, and in conventional shoes as shown in FIG. 24. However, again for emphasis, internal linkage mirrored arch spring 107 of FIG. 13 as made monolithic by as shown by cut-out monolithic mirrored spreader linkage 183 in FIG. 15 is the most preferred optimal spring herein because this internal linkage impinges the outer mirrored arch spring, and there is a distinct practical advantage of not needing to make tensioned connections. The fact that this linkage can be injection molded, in combination with the fact that the outer mirrored arch spring element can be easily fabricated of fiberglass (an order of magnitude stronger/lighter than TPUs) makes the monolithic version of internal linkage mirrored arch spring 107 the clear winner. Again, the force curve can be made completely optimal, as explained for FIG. 12, since this design is easily to pre-load and with auxiliary springs to ensure a constant total force curve near full compression.

The analogous design to band tensioned linkage spring 340 of FIG. 21 is monolithic band tensioned linkage spring 372, which is shown in its compressed state with the view of compressed monolithic band tensioned linkage spring 374. Monolithic quad links 354 connect to their side mirrored images via monolithic vertical necked-down vertices 356. The side connections comprising second necked restraint 376, band end loop 304 (and hollow rectangular band retainer pin 300 on the right side) correspond to those same or equivalent elements in FIG. 20. Likewise the side connections comprising third necked restraint 378, band end loop 304, and hollow rectangular band retainer pin 300 on the left side correspond to those same or equivalent elements in FIG. 20. In this design, the link elements are preferential made of injection moldable material such as TPUs (e.g., Pellethane or PEBAX), while the spring elements are preferentially made of fiberglass. This is a fully optimal spring in the sense defined herein provided there are auxiliary springs incorporated as explained just above. Note that the monolithic side pivoting arrangement of monolithic tensioned linkage spring 350 can as well be used with a tension band as was done with monolithic band tensioned linkage spring 372. Basically, tension band 302 replaces monolithic curved springs 366, and the linkage elements are monolithic with the spring tension elements—in which case both need to be a more compliant material such a TPU with its attendant energy hysteresis loss.

FIG. 23 is a schematic side view of monolithic nested tensioned linkage spring 380 which is very similar to monolithic tensioned linkage spring 350 of FIG. 22 except that two nested curved springs are used. Side vertex connection section 370 now diverges into 1st nested curved spring 382 and 2nd nested curved spring 384, each of which is pivotally connected to its mirrored image by monolithic tip connection sections 368. Otherwise, the elements are the same as for FIG. 23, and the discussion is the same. The reason for nesting curved springs is that the spring system can be stronger, by a factor of two or three practically speaking. The disadvantage is that the total spring height is higher and the compression ratio is lower. However, this ratio does not change significantly in view of the fact, for the fiberglass curved springs preferred in the instant invention, that the arm thicknesses are so small (of the order of 0.05″ to 0.2″ as shown in Table 1). This increase in nested spring strength is important for the gear change capability of FIG. 26.

FIG. 24 shows schematic side views and a top view of optimal springs in a conventional shoe, which means shoes that do not feature the heel-pop capability for enhanced heel-lift. The use of optimal shoes in conventional shoes is the fourth embodiment of the invention because it can be used in all shoes, thereby providing the health benefits of significantly reduced maximum impact force to the people of the world. Constant thickness shoe 411 comprises shoe upper 1 fixably attached to the top of constant thickness sole 405. Constant thickness shoe 411 comprises shoe upper 1 fixably attached to the top of constant thickness sole 405. Tapered shoe 413 comprises shoe upper 1 fixably attached to the top of tapered thickness sole 407. One or more internal linkage mirrored arch springs 107 can be located in both constant thickness sole 405 and tapered thickness sole 407, e.g. Likewise is true for sideways internal linkage mirrored arch springs 401, which are the same as internal linkage mirrored arch springs 107 except that they are rotated about the vertical by 90 degrees, in which case with they resist forward translation of footplate 3 with respect to ground plate 5. Both fig views have toe pivot 403 so that both constant thickness sole 405 and tapered thickness sole 407 can articulate at the toe joint. In tapered thickness sole 407, sideways internal linkage mirrored arch spring 401 features on its top side hard elastomer top to compensate for the small difference in sole height from the front side to the back side of sideways internal linkage mirrored arch spring 401. Another type of spring that can be used is mirrored arch spring 80. However, this has a linear force curve. The novel aspect here is the use of optimal springs. There have been a number of optimal springs shown in the instant invention. Any optimal springs shown herein that are variations of curly v-springs and of mirrored arch springs can be used in constant thickness sole 405 or in tapered thickness sole 407, because these compress vertically.

If the sole is thick and of constant thickness, there will be a problem with toe sink, as was explained for FIGS. 1-9. Several things can be done to solve this problem. Unfortunately, the anti-toe-sink mechanism of the heel-pop shoes of figs cannot be used because it requires forward translation of footplate 3 with respect to groundplate 5 to work. Using a tapered sole helps, or conventional toe stop 412 can be located under toe plate 7, say half the sole height, for example. This is only shown for constant thickness sole 405, but it can also be used in tapered thickness sole 407. Also, a stiff spring can be used under the very front of toe plate 7. In either case, the runner's toes are bent up at full sole compression. Having the toe bent up is tolerable, and there is definitely no toe sink during toe-off. And, there is actually a benefit in that the toes can push off from a higher point during toe off.

The top view of conventional shoe with optimal springs 409 (which corresponds to both constant thickness shoe 411 and tapered shoe 413) shows possible locations of the various springs. Since the optimal springs herein are all based on curved spring elements, they can all be sliced to any width. This means that the widths can be all across the shoe or any combination of one or more springs of smaller widths. Just as an example, internal linkage mirrored arch springs 107 are shown four abreast and then three abreast. Sideways internal linkage mirrored arch spring 401 is also shown. At zero compression, this is touching footplate 3 and groundplate 5 along a center line longitudinally oriented. Mirrored arch spring 80 is shown below toe plate 7, but it could be any optimal spring. Note well that any of the component springs in an assembly of springs for a shoe—in FIG. 24, or in FIGS. 1-9 for heel-pop shoes, or in FIG. 25 for gear change in shoes—(1) can be located anywhere underfoot or around the outside of the foot, (2) can have any stiffness value of force curve, and (3) can be oriented at any angle. The decision on how to use each component spring in the assembly depends on considerations of structural optimization, stability, and functionality issues such as pronation. In addition, these component springs can easily be held together one to the other with bridging plates so that they can be inserted into a shoe sole as a cartridge, in a manner obvious to one of ordinary skill in the art.

The essential benefit of the second and fourth embodiments of the invention (the second being optimal springs and fourth being their use in conventional shoes), where the optimal springs embodiment includes both optimal springs of the instant invention and the method to construct these optimal springs, is that the maximum impact force value is reduced by as much as 40% as explained for FIG. 12. The optimal springs disclosed in the instant invention are novel, as is their use in any shoe, conventional or heel-pop is novel. Also, the method to achieve a desired optimized force curve with a minimum value for the maximum force on the curve explained for FIG. 11 and FIG. 12 and table 1 (for the optimal sole energy storage) is also novel and can be used in any type of shoe, both conventional and heel-pop. There will also be some energy return for optimal springs in conventional shoes, but not nearly as much as for heel-pop shoes as was explained earlier. All of these designs can be pre-loaded. Also, many of these designs can be used in various combinations with each other—with equivalently optimum force curves. And, each design can be refined and optimized by varying the shapes of the spring elements, the various thickness profiles, the hinge means, the geometries, and the configurations. While various materials can be used to fabricate these optimal springs, the preferred material for the spring elements for most applications, and certainly for shoe applications, is fiberglass.

In order to understand the entries for nested springs in Tables 2 and 3, consider the following. For example, FIG. 23 shows monolithic nested tensioned linkage spring 380. Also, note that it is possible in like manner to nest all of the optimal spring described herein. Since the thicknesses of the arms of all variants of the arch spring are small (˜ 1/16″ for both the curly v-spring and the mirrored arch spring; ˜1.8″ for the one-sided curved spring), it makes sense to nest the springs when greater spring strength if required because the compression ratio of the nested springs is still quite high. With regard for the entries for spring strengths in Tables 2 & 3, it is assumed that a nested spring is twice as strong as an un-nested spring. Actually, if more than two levels nesting are done, it could be more than twice as strong, again at the price of increasing the fully compressed thickness of the shoe sole. These tables also show that the various springs for the three types of shoes do not have to fill the entire sole width. For example, the spring system for the curved-spring heel-pop shoe is 2.8 times stronger than needed. This means that only 38% of the sole width need be used—presumably 18% on either side with a 64% of width gap in the middle. Also, the spring strength on either side can easily be varied (simply by altering the spring width on one side) to make the spring strength asymmetric.

In like manner, the above-described procedure can be used for conventional shoes, in which case the spring system is three times what is needed (shown in Table 2 as 300%). If one were to nest the springs, even less of the sole width would be needed for the spring system. For example, for the curved-spring heel-pop shoe, only ˜19% of the sole width need be used with one level of nesting—9.5% on either side. Furthermore, in view of the fact that the spring material is fiberglass, the spring weight for each shoe is very light, 4 oz for the curved-spring heel-pop shoe and 3.5 oz for a conventional shoe. It is rare to find a conventional running shoe that deflects more than a quarter of an inch, and even then it is only the heel that deflects. With the novel arch springs described herein, the sole deflection of 2 inches is eight times greater, over the entire sole, and the spring weight is only 3.5 oz. That's quite a bargain. Note also, as an alternative to locating the narrow springs only on either side, that narrow strips of springs could also be located in the center region. This would prevent the center region (laterally speaking) from caving in, which would permit the footplate structure to be lighter.

Now we have the information needed to address the fourth embodiment of the invention, namely a method to tune the spring system strength to the requirements of the individual user—during manufacture. Although this method applies to any springs used in shoes, the arch springs described herein are preferred because their strengths can be finely chosen (tuned) by cutting them to a particular width. In other words, this method can be used in manufacture to provide particular fixed spring strength finely tuned to the requirements of a particular user. In addition, a shoe company could manufacture a shoe with a particular minimum spring strength, using springs located on either side within the sole of the shoe. Then add-on springs of variable strengths could be inserted in the vacant center section of the shoe sole so as to tune the shoe for an individual's needs. In this way, standard shoes can be mass produced for a limited range of spring strengths, as is now done, and then spring inserts can be sold to tune the shoe for an individual. These inserts can easily be snapped into the center region of the sole in a manner obvious to one of ordinary skill in the art. Or, a shoe owner could buy a range of springs to cover different uses such as walking, jogging, running, or sprinting. Or, if the owner's weight changes a lot, she can simply change the center spring to fine tune her shoes to her new weight. Various metrics can be used to tune the spring system for the user—first, just his or her weight, or his gait range such as walking or jogging, or the results of a force platform study of his or her ground reaction force requirements. This equipment should be standard fare in shoes stores practicing the spring tuning method described herein.

Included in the second (optimal springs) embodiment of the invention is a method to tune the spring system strength to the requirements of the individual user—during manufacture. In order to better understand how to tune the spring system, it behooves us to explore in some detail the locations and strengths of these springs. First a very important part of the method must be understood. The shoe inventions herein work best with substantially greater sole deflections (˜1-3 inches) than what is found in most running conventional shoes (˜⅛ to ⅜ inches). Note well, that in order to achieve the full benefits of any shoes, in terms of foot impact reduction and energy return, the sole should fully deflect (e.g. by the full 2 inches). Again, if the compressing sole bottoms out or only deflects partially, the shoe will not provide the full benefits of both impact reduction and energy return for the user. Needless to say, virtually none of the conventional shoes provide the above benefits to their users to the full potential.

FIG. 25 shows the schematic top view of possible spring locations for a shoe. In particular, it shows the possible underfoot locations and area sizes of the curved springs used for precise spring tuning for the optimal springs embodiment, as well as the side locations for the fifth embodiment for gear change. Even so, FIG. 25 will serve to describe the locations of the springs for the other shoes described herein, namely the parallelogram heel-pop shoe and the conventional shoe. The spring locations are in two possible types of locations—under the foot (in the sole) and on the sides of the foot. The shoe is divided into three sections from front to back: toe section 400, forefoot section 402, and heel section 404. Foot 418 is for nominal size 8 US. As such, the nominal width of display front curved spring 410 is 4 inches, and the nominal width of display rear curved spring 408 is 3 inches. The nominal width of inside curved spring 412 and of outside curved spring 406 is 1 inch. Boundary for inside heel clearance 416 defines the area inside that boundary for which there is heel clearance as the foot (and especially the heel) in the air passes the planted foot during walking or running. Base inset 414 shows that the heel is narrower than the forefoot. Toe hinge 420 defines the front edge of display front curved springs 410, and it defines the front of the adjacent inside curved spring 412 and of the adjacent outside curved spring 406. There are three tables which provide data for spring strengths to be used for optimizing the spring system strengths in shoes: Table 1. Comparison of Spring Strength vs Deflection for Various Materials, Table 2. Summary of Spring Strengths for Heel-Pop Shoes and for Conventional Shoes, and Table 3. Calculation of Spring Strengths for Heel-Pop Shoes and for Conventional Shoes.

Accordingly, for the heel-pop shoes of FIGS. 1-9, e.g., in view of FIG. 25, there are 4 inches of underfoot spring width available from forefoot section 402 and 3 inches of underfoot spring width available from heel section 404. That is a total of 7 inches of underfoot spring width. At the same time, there are 2 inches of side spring width available from forefoot section 402, and there are 2 inches of side spring width available from heel section 404. As shown in Table 2. Summary of Spring Strengths for Heel-Pop Shoes and for conventional Shoes, like values for spring width are used to calculate the available strengths for three types of shoes, namely for curved-spring heel-pop shoes, for parallelogram heel-pop shoes, and for conventional shoes. These spring strength calculations are done for the underfoot springs and for the side springs. For example, the first entry in Table is for curved-spring heel-pop shoes which use curved springs (see FIGS. 4-6). Non-linear finite element analysis (fea) was done for these springs to calculate the maximum spring strength achievable at a 2″ spring deflection (height) as 180 lbs for a 1″ width spring. As Table 1 shows the preferred material by far is fiberglass. Thus, the spring strength for 7 inches of available spring width is 1260 lbs as shown in Table 3. Assuming that a 150 lb runner is running with a maximum ground reaction force of 3 gees, 450 lbs of spring strength is needed, the available force is 2.8 times 450 lbs, or 280%. In like manner, the available spring strengths are calculated for parallelogram heel-pop shoes of FIGS. 7-9 which use curly v-springs 96 or the aforementioned rolling version of mirrored arched spring 80, and for conventional shoes which used a combination of mirrored arch springs 80 and curly-v-springs 96. The results of the spring strength calculations of Table 2 are summarized in Table 3. Those entrees related to gear change will be discussed below in the passages describing gear change. With reference to FIGS. 7-9 for parallelogram heel-pop shoes, which can use either three curly v-springs 96 or which can use the aforementioned rolling version of mirrored arched spring 80, and with reference to FIG. 25, there are 4 inches each of available spring width from the two curly v-springs 96 of forefoot section 402 and 3 inches of available spring width from heel section 404, for a total of 11 inches. Each inch of spring width provides 90 lbs, so the total spring strength is 990 lbs, or 220% of what is needed. In like manner for conventional shoes, with reference to FIG. 25 and tables 2 and 3, springs can now be located in toe section 400 both underfoot and on the sides. Mirrored arch springs 80 are used in forefoot section 402, while curly v-springs 96 are used in toe section 400 and heel section 404. Thus, there are 4 inches of available spring width in forefoot section 402 and 7 inches of available spring width from toe section 400 and heel section 404. This provides a total of 1350 lbs of spring strength, or 300% of what is needed.

The fifth embodiment of the invention is a structure and method to automatically change the spring stiffness of the shoe while the user is running or walking. This is referred to herein by the short-cut term of “gear change” of the shoe because that term is more easily understood. We have already seen where side springs can be located outside the shoe sole in the discussion of FIG. 25. Gear change cannot be achieved by using only display front curved spring 410 and display rear curved spring 408 because these are underfoot. This means that these springs must always act to resist sole compression. In the case of side springs, it is possible to disengage them so that the runner's foot, via footplate 3, does not act against them. Thus, by engaging and disengaging these side springs, the shoe gear (effective stiffness) can be changed.

Consider the following example of the side spring strength needed to change gears by a factor of three. Basically, this means that two-thirds of the total spring strength needs to be provided by the side springs. The total spring force is 450 lbs (3 gees for a 150 lb runner). Thus, the side springs must provide 300 lbs of force. With reference to Table 3, this explains the value of 300 lbs used there—that must be supported by the side springs. Note again that we have 2.4 times as much spring force as is needed for both the curved-spring heel-pop shoe and conventional shoes, and 1.8 times as much spring force as is needed for conventional shoes. Notably, these values are doubled to 4.8 and 3.6 with spring nesting. Thus, the use of fiberglass for these springs makes possible a gear change ratio that is quite acceptable since these values exceed the above value of a factor of 3. So now that we know we have enough spring strength, how do we change gears? FIG. 26 shows a schematic drawing of a mechanism to accomplish this goal, in three views for one side of the shoe. Of course, this mechanism is on both sides of the shoe, and the gear change must be synchronized on both sides.

FIG. 26 shows schematically a side view, a top view, and a front view of gear change side spring assembly 450, and it shows schematically a side view and a front view of compressed gear change side spring assembly 452. These are located on either side of the shoe within the constraints indicated by FIG. 25. Spring frame 458 is rigidly attached to the side of footplate 3; it extends upward to rigidly connect to drive shaft 468 which extends out toward the side. Three drive bars 472 are rotatably connected to drive shaft 468 via bar holes 460, and these hang down from drive shaft 468. Directly below each drive bar 472, there is located side mirrored arch spring 462, which is mounted on top of groundplate 5 and which comprises a top half and a bottom half rotatably connected to each other by arch spring pivot 464. For example, a 1″ wide spring could be sliced into three springs, 1/3″ wide. Lock hole 466 is in the top of drive bar 472 above bar hole 460, and it is oriented perpendicular to it.

Compressed gear change side spring assembly 452 shows the configuration in which two of the three side mirrored arch springs 462 have been compressed, while the third one has been disengaged and, hence, not compressed. In other words, a particular total spring strength has been selected, which corresponds to a particular gear having been selected. In particular, the two outside drive bars 472 have driven downward the two outside compressed mirrored arch springs 476 below them. Note that compressed mirrored arch spring 476 is simply a side mirrored arch spring 462 that has been compressed. At the same time, inside drive bar 472 has disengaged so that its side mirrored arch spring 462 has not been compressed. The method of disengagement is shown in assembly the top view and in the side view of compressed gear change side spring assembly 452.

Housing 480 is rigidly connected to the top of spring frame 458, and it houses length actuator 482, which in turn moves shaft bar 478 forward and backward. There are three lock shafts 470, one for each drive bar 472. Each lock shaft 470 is rigidly attached to shaft bar 478 at staggered lengths so that each of them passes through its respective lock hole 466 (in drive bar 472) at different times as shaft bar 478 is moved forward and backward. When lock shaft 470 enters lock hole 466, drive bar 472 cannot rotate out of the way of side mirrored arch spring 462, in which case drive bar 472 drives side mirrored arch spring 462 downward to the compressed state of compressed mirrored arch spring 476. Otherwise, drive bar 472 is free to rotate to the configuration of rotated drive bar 474, in which case its side mirrored arch spring 462 is not compressed. That is to say the gear is not engaged.

The other elements of the gear change mechanism are microprocessor 484 and force sensor 486. These are electrically connected to length actuator 482. These elements are shown only in the top and side views, in schematic fashion. Microprocessor 484 controls the motion of length actuator 482 so as to change gears, and it could be located in a number of places, but probably it would be mounted on spring frame 458 close to housing 480. Shoe power source 488 can also be located in housing 480. Force sensor 486 is located at the bottom of groundplate 5 so that it can measure the ground reaction force of running or walking. The gear change method proceeds as follows. Its function is to maintain the total spring strength at a level at which sole deflection is maximized. Micro processor 484 has a look-up table which looks at a measured force and sends a signal to length actuator 482 to move to a position at which the optimal gear (that is equivalently, the optimum number of engaged drive bars 472) is selected for the very next stride. Remember that an engaged drive bar 472 corresponds to a compressed mirrored arch spring 476. The example shown, with three side springs, could permit the following gears. The weakest gear (total spring strength) would be the strength of the underfoot springs, e.g. 1 gee. Then, each individual side spring could add 0.7 gees, in which case the four gears would be 1 gee, 1.7 gears, 2.4 gees, and 3.1 gees. Remember from tables 2 and 3 that there is plenty of strength to achieve these spring strengths with the various combinations of arch springs described herein. Thus, the gear change allows the sole to fully compress for four levels of impact force, and the performance of the shoe is automatically optimized over a range of running impact forces.

FIG. 27 shows schematic side views of a tensioned linkage rotating arms curved spring. That is, it shows schematic side views of an optimal spring for a rotating arms joint which is the third embodiment of the invention. Tensioned links rotating arms curved spring 500 comprises top arm 510 hingeably connected to bottom arm 512 by arm hinge 514. Compressed mirrored double linkage curved spring 516 is hingeably connected to bottom arm 512 and top arm 510, and it comprises mirrored double linkages 131, which comprise curved spring 127 hingeably connected to top arm 510 (e.g.) and hingeably connected to one of the two double links 125. The two double links 125 are hingeably connected by double hinge 126, and the other double link 125 is hingeably connected to the other end of curved spring 127 where it hingeably connects to top arm 510. Adjust spring 133 is tethered to arm hinge 514 by adjust tether 504, and it is tethered to top arm 510 by arm tether 508 via one of its curly v arms. Refer to curly v-spring 96 of FIG. 10. Any of the other curly v type versions of optimal springs herein can be used as well. Curved arch pivot 518 connects the mirrored curved springs 127. Monolithic arch hinge 187 of FIG. 15 can be used here as well as conventional hinge with shafts and bearings. The view of compressed mirrored double linkage curved spring 516 shows that double linkage 131 has compressed so that the mirrored double hinges are impinging, and thereby double linkage 131 is spreading curved spring 127 to resist the folding of top arm 510 with respect to bottom arm 512 about arm hinge 514. Also, adjust spring 133 is now engaging top arm 510 and bottom arm 512 to prevent the torque exerted by tensioned links rotating arms curved spring 500 (to resist the folding about arm hinge 514) from going to zero. Adjust tether 504 prevents adjust spring 133 from sliding away from arm hinge 514 during compression. Thus, the torque force curve can be made constant, in a manner analogous to how the force curve in FIG. 14 remains constant for 1^(st) double link-spread curved spring 122. The advantages for the various optimal springs herein also apply for tensioned links rotating arms curved spring 500. The maximum torque value is minimized for a given energy necessary to fold the arms. This reduces the wear and tear on the device, and it minimizes the impact force in running for the application of ankle joints or knee joints.

In a manner analogous to the gear change capability of FIG. 26, multiple tensioned links rotating arms curved springs 500 can be arranged side by side as torque elements in such a manner that one or more can be engaged or disengaged to in effect change hears for the spring resisted folding device (namely tensioned links rotating arms curved spring 500). Likewise, sensors can be used to determine when the spring resisted folding device has the resistance elements engaged. For applications such as an ankle joint or a knee joint, all resistance elements must be disengaged during the swing phase when the runner's feet are not in contact with the ground. A microprocessor uses this sensor information to determine when these resistance elements should be re-engaged just before foot impact, and how many are re-engaged. A ratchet device needs to be incorporated in case the folding joint does not always straighten the same amount before foot impact. That is, the knees may remain more bent at heel-strike. All these adaptations of the gear change device of FIG. 26 can be made by one of ordinary skill in the art, and all of the features of the gear change device of FIG. 26 can be adapted to a gear change application of tensioned links rotating arms curved spring 500. Note that it is possible to replace curved spring 127 with tension band 302 of FIG. 20, e.g. —in which case it would be connected in a manner similar to that shown in FIG. 20 or in FIG. 22—in a manner obvious to one of ordinary skill in the art. The hard part is to find a material which does not have hysteresis energy loss, as has been mentioned for TPU-like materials herein. A very interesting candidate material is disclosed by Pratt in U.S. Pat. No. 7,906,191 of Mar. 15, 2011. He discloses a composite material in which the fibers in a particular layer are laid down in sinusoidal waves transversely oriented within the plane of the layer. This means that a composite of wavy fibers can be stretched considerably without breaking the fibers. For fiberglass the elongation limit is of the order of ˜4-5%, and for carbon fiber the elongation is ˜1-2%. That is not enough for the requirements of tension bands 302 herein. By incorporating the wavy structure it is possible to increase the amount significantly. However, Pratt's goal was to provide damping of structures made of his wavy composite material for bending applications, not for stretching. Quoting from Pratt's patent, “The terminology CWCV (continuous wave composite viscoelastic) will be used to define a composite structure which uses at least one layer of wavy composite material having viscoelastic properties (or ‘anisotropic viscoelastic’); or at least one layer of wavy composite material combined with at least one layer of viscoelastic material either in a sandwich construction or adjacent construction.” Also, “Damping is induced in the structure primarily by the differential shearing of the viscoelastic layer by the wavy composite laminate. This shearing induces elongation of the long chain polymers in the viscoelastic which in turn generates heat, causing energy loss in the structure. This energy loss accounts for the primary source of damping in the structure.” Of course, for the purpose of the instant patent, the goal is to have a minimum of damping or energy dissipation. However, it is possible to make a continuous wavy composite without the viscoelastic layers. This then is the preferred material for the tension bands 302 in FIG. 7, FIG. 20, and FIG. 22 herein. Call it a continuous wave composite (without the term viscoelastic). The important advantages are the strength and the low energy hysteresis loss (sans the viscoelastic layers). It may be possible here to use carbon fiber composite as well as fiberglass fiber.

In summary, the optimized shoe invention comprises five embodiments and two methods to optimize both the performance and comfort of footwear walking and running for people and for robotic, prosthetic and orthotic applications. First, there are three versions of enhanced heel-lift heel-pop shoes for significant energy return much higher than what is achievable with conventional shoes. Second, to minimize foot impact there are ten enhanced optimal springs. Third, for ankle and knee joints there is a rotating-arms enhanced optimal spring. Fourth, said enhanced optimal springs are incorporated into conventional shoes. Fifth, there is an automatic gear change mechanism to change the sole spring stiffness so that the sole is always is close to full compression so that the performance and comfort is always optimal. The optimal force curve method to minimize foot impact requires optimal springs with a pre-loaded constant force curve and a means to calculate, measure, and adjust the optimal total sole energy for a particular user for a particular type of running or walking. The shoe tuning method provides a means to measure and adjust sole energy of shoes by precise slicing of 2D sole springs during the manufacture of said shoes or by the use of precise insertable 2D springs—based on the fact that the sole energy absorbed at full deflection by the optimized springs of the instant invention is linearly proportional to a scientifically chosen value of sole thickness. The sum total of these five embodiments and two methods constitutes an improvement in footwear that will hopefully revolutionize the industry—if the instant inventor might be allowed a brief fit of hyperbole after all these years of hard work—with all due apologies, of course. Finally the usual proviso applies, namely that the many designs of the invention disclosed can be combined or varied to encompass many variations which are still covered by this patent and which combinations and variations are obvious to one of ordinary skill in the art.

TABLE 1 Comparison of Spring Strength vs Deflection for Various Materials Fiberglass Carbon Fiber PEBAX 5533 Titanium d f t d f t d f t d f t First Part for the Curly V-spring .5 23 .012 .5 2.2 .004 .5 1.44 .031 .5 2.5 .004 1 46 .024 1 4.4 .008 1 2.88 .061 1 5 .009 2 92 .048 2 8.8 .015 2 5.73 .123 2 9.9 .018 5 230 .121 5 22 .038 5 14.3 .31 5 24.9 .044 20 920 .484 20 87.8 .154 20 57.3 1.2 20 99.5 .177 50 2300 1.21 50 220 .384 50 143 3.1 50 249 .443 100 4600 2.42 100 439 .769 100 287 6.1 100 497 .885 Second Part: for the Curved Spring (the bottom half of the Curly V-Spring) .5 46 .024 .5 4.4 .008 .5 2.88 .061 .5 5 .009 1 92 .048 1 8.8 .015 1 5.73 .123 1 9.9 .018 2 184 .096 2 17.6 .030 2 11.5 .24 2 19.8 .036 5 460 .242 5 44 .076 5 28.6 .61 5 49.7 .089 10 920 .484 10 87.8 .154 10 57.3 1.2 10 99.5 .177 20 1840 .968 20 176 .308 20 115 2.4 20 199 .354 50 4600 2.42 50 439 .769 50 287 6.1 50 497 .885 100 9200 4.84 100 878 1.538 100 574 12.2 100 995 1.77 d = deflection in inches; f = load force in lbs; t = thickness in inches Assumes a spring width of one inch.

TABLE 2 Summary of Spring Strengths for Heel-Pop Shoes and for Conventional Shoes % Available % Available Strength Strength Underfoot for Gear Change Curved-Spring 280% 240% Heel-Pop Shoes 560% 480% (with nesting) Parallelogram 220% 180% Heel-Pop Shoes 440% 360% (with nesting) Conventional 300% 240% Shoes 600% 480% (with nesting) This assumes a 150 lb runner and 3 gees (450 lbs) as the maximum ground reaction force; the spring material is fiberglass. The sole deflection is a nominal 2 inches.

TABLE 3 Calculation of Spring Strengths for Heel-Pop Shoes and for Conventional Shoes Underfoot springs must support 450 lbs for curved-spring heel-pop shoes one-sided arch springs 1″ >180 lbs 7″ > F = 1260 lbs % = 1260/450 = 280% for parallelogram heel-pop shoes curly v-springs  1″ >90 lbs 11″ >  F = 990 lbs % = F = 220% 990/450 for conventional shoes Mirrored arch springs 1″ >180 lbs 4″ > F = 720 lbs (at forefoot section) & curly v-springs  1″ >90 lbs 7″ > F = 630 lbs (at toe & heel sections) Sum = 1350 lbs % = 1350/450 = 300% With gear change, side springs must support 300 lbs for curved-spring heel-pop shoes one-sided arch springs 1″ >180 lbs 4″ > F = 720 lbs % = 720/300 = 240% for parallelogram heel-pop shoes curly v-springs  1″ >90 lbs 6″ > F = 540 lbs % = 540/300 = 180% for conventional shoes Mirrored arch springs 1″ >180 lbs 2″ > F = 360 lbs (at forefoot section) & curly v-springs  1″ >90 lbs 4″ > F = 360 lbs (at toe & heel sections) Sum = 720 lbs % = 720/300 = 240% This assumes a 150 lb runner and 3 gees (450 lbs) as the maximum ground reaction force; the spring material is fiberglass. The sole deflection is a nominal 2 inches. 

Having thus described the invention, what is claimed as new and described to be secured by Letters Patent is:
 1. An optimized shoe for walking and running by humans and robots, wherein the applications for humans include normal human use, prosthetics, and orthotics, wherein the stance period is divided into a compression period and an expansion period, wherein the entity wearing and using the shoe is called the user, wherein said expansion period comprises a heel-lift period and a toe-off period, wherein said optimized shoe comprises a heel-pop shoe which comprises a compressible sole, a top load surface on the upper side of said compressible sole further comprising a footplate hingeably connected to a toe plate by a toe hinge, a bottom load surface called a groundplate on the lower side of said compressible sole, wherein said compressible sole further comprises a toe section, a forefoot section, and a heel section, wherein said compressible sole further comprises a spring system which resists compression and which stores the impact energy of compression and a heel-pop mechanism also called an enhanced heel-lift mechanism to lift said heel section during said heel-lift period by a distance that is substantially greater than the distance over which said heel section is compressed during said compression period which distance is called herein enhanced heel-lift, wherein said heel-pop mechanism provides energy return that is substantially greater than that of conventional shoes which do not have said heel-pop mechanism, wherein the significance of said energy return is that the metabolic energy cost of running is substantially reduced.
 2. The optimized shoe of claim 1 wherein the resilient elements of said optimized spring system are made of fiberglass composite, wherein fiberglass is the significantly preferred material because it has very low mechanical hysteresis loss of approximately one to two percent as compared to approximately 20-50% for injection moldable materials such as thermoplastic polyurethanes (for example, pellethane 2363 or PEBAX 5533), wherein any other material with critical parameters for flexibility and bending strength which are similar to those of fiberglass can also be used, wherein the critical parameter for flexibility for said arch springs is the elongation limit of either the fiber or of the geometrical construction of the fiber.
 3. The optimized shoe of claim 1 wherein said spring system comprises an optimal spring system with an optimal force curve, wherein the force-curve optimization goal for said optimal force curve is to maximize the amount of energy absorbed (namely the area under the force curve) for a given said maximum force point, wherein the first part of a method to achieve a desired optimal force curve is to pre-load it and the second part is to vary the spring structure and shape so as to achieve a softer, more constant force curve, wherein the components of said optimal spring system are pre-loaded so that the force at the beginning of the optimal spring compression is a predetermined value (for example one-third the force value at full spring compression), wherein the work done by said spring system is the area under the curve of the force versus the spring deflection, wherein said work is accomplished with a reduced value of the maximum force point value as compared with the maximum force value point when there is no pre-load and as compared with a linear force curve, wherein said pre-load is accomplished with a physical restraint such as a tether or such as a structural restraint wherein the first criterion for said optimal force curve is to pre-load said spring system and the second criterion for said optimal force curve is to create a geometry so that the slope of the force curve decreases or even approaches zero throughout the latter said sole compression.
 4. The optimized shoe of claim 1 wherein said spring system comprises a set of enhanced arch springs each of which is constructed from one or more arch spring types, wherein each said arch spring type represents a combination of elemental curved springs in different orientations, wherein said elemental curved spring is also called a curved arm and it is a curved spring which substantially flattens to a flat plate under full compression, wherein the first arch spring type is said elemental curved spring, wherein the end of said curved arm (which is horizontal and approximately parallel to the adjacent base load surface) is called the base end and the end of said curved arm that is approximately perpendicular to or diagonal with respect to the adjacent tip load surface is the tip end, wherein the full compression thickness at full compression of said elemental curved spring is the thickness of said curved arm, wherein the approximate shape of said elemental curved spring is a quarter of a circle although the curvature may be somewhat different, wherein the elemental spring height of said elemental curved spring is approximately the radius of said quarter of a circle, wherein said elemental full compression thickness is substantially smaller than the elemental spring height possible by a factor of ten to twenty, wherein the first arch spring type is simply said elemental curved spring, wherein said tip load surface freely translates horizontally with respect to said base load surface, wherein the spring strength comparisons for said elemental curved spring are as follows, wherein the spring strength using fiberglass composite is approximately ten times stronger than the spring strength using carbon fiber, wherein the spring strength using fiberglass composite is approximately sixteen times stronger than the spring strength using said injection moldable materials, wherein the spring weight using fiberglass composite is approximately twelve times lighter than the spring weight using carbon fiber composite, wherein the spring weight for fiberglass composite is approximately eight times lighter than the spring weight using said injection moldable materials.
 5. The optimized shoe of claim 1 wherein said spring system comprises one of more said arch spring types, wherein the second said arch spring type is called an arch spring in which two said elemental curved springs are combined to form the shape of an arch, wherein the left side of said elemental curved spring is the mirror image of the right side of said elemental curved spring constructed about the vertical line at the junction of the opposing said base ends, wherein the arch center is located where the base ends of the opposing said elemental curved springs join, wherein the third said arch spring type is called a mirrored arch spring in which case the upper concave downward said arch spring is mirrored about the horizontal line just below the opposing said tip ends of the upper said arch spring, wherein the said arch centers of the upper and lower said arch springs are loaded by their adjacent mirrored load surfaces causing the opposing said tip ends to move outward horizontally as said mirrored arch spring fully flattens, wherein said mirrored load surfaces do not translate horizontally with respect each other and instead they move vertically and directly toward each other during said spring compression, wherein the fourth said arch spring type is called a rolling mirrored arch spring in which case the top and bottom of said mirrored arch springs have a circular shape in which case said rolling mirrored arch spring can roll somewhat while it is being loaded by two surfaces which are translating horizontally with respect to one another, wherein the fifth said arch spring type is called a half mirrored arch spring in which case said mirrored arch spring is cut in half along a vertical line though its center when viewed from the side, wherein the sixth said arch spring type is called a curly v-spring in which case said elemental curved spring is combined with its mirrored image also called an inverted said elemental curved spring to form said curly v-spring which looks like the letter V turned on its side with each of its arms being curled in the shape of said elemental curved spring, wherein the seventh said arch spring type is called nested arch springs in which one or more said arch spring types is or are nested within another arch spring type to form a nested arch spring at one or more levels of nesting, wherein the base of said elemental arch springs are offset in the vertical direction with respect to each other so that when said nested arch spring fully compresses, each component said elemental curved spring is approximately horizontal along its entire length, wherein the total spring strength of said nested arch spring is increased over that of a single said arch spring albeit at the cost of an increase in the thickness of said nested arch spring at full compression, wherein all above said arch spring types and more complex variations made from them have similar force curves and behaviors to the force curves of said elemental curved springs of which they are constructed.
 6. The optimized shoe of claim 5 wherein said arch spring types comprise spring elements, linkage elements, and hinges, wherein said spring elements and said linkage elements are connected to each other with hinges, wherein one or more said hinges are conventional cylindrical hinges comprising shafts and bearings.
 7. The optimized shoe of claim 3 wherein said optimal spring system comprises an enhanced optimal spring system which is constructed of said arch spring types, wherein said enhanced optimal spring system is designed to optimize the force curve for devices such as footwear where it is advantageous to minimize the maximum force point along the force curve (especially when there is an impact force) on said user, on the structural elements of said spring system and on the device within it is incorporated, wherein the force-curve optimization goal for said force curve optimized spring is to maximum the amount of energy absorbed (namely the area under the force curve) for a given said maximum force point, wherein the first part of a method to achieve a desired optimized force curve is to pre-load it and the second part is to vary the spring structure and shape so as to achieve a softer, more constant force curve, wherein these changes in force curve can reduce said maximum force value by 25% to approximately 40% as compared to a spring system with a linear force curve, wherein there are two classes of enhanced optimal spring systems, namely an enhanced fully optimal spring system where the force curve becomes approximately constant during the latter part of compression and namely an enhanced partly optimal spring system where the slope of the force curve decreases to approximately half of its initial value during the latter part of compression, wherein when a non-linear finite element analysis is done to determine the maximum allowable thickness (and hence the maximum possible force) of said curved arms within the stress limits of the material of which said curved arms are made, the total energy absorbed (work done) per unit area by each said arch spring is linearly proportional to the full deflection value which is the deflection at full compression so that it is easy to achieve a particular total energy absorbed by simply choosing the corresponding said full deflection value, which means that the only way to change said total energy absorbed (work done) per unit area is to change said full deflection value, wherein the impact energy of running is absorbed by the compression of said compressible sole with the sole compression energy and by the compression of the leg of said user with the leg compression energy, wherein the third criterion for optimization of said sole compression energy is to determine the optimal sole compression energy by experiment and then to realize said optimal sole compression energy by choosing the corresponding particular said deflection value, wherein one or more said hinges are necked-down living hinges which permit a continuous monolithic construction between adjacent ones of said linkages elements and said spring elements.
 8. The optimized shoe of claim 7 wherein said enhanced fully optimal spring system comprises first enhanced fully optimal spring system which is also called an internal linkage mirrored arch spring system which comprises monolithic mirrored arches, wherein said monolithic mirrored arches belong to a tension spring class of tensioned springs which comprise said elemental curved springs and tension band springs, mirrored spreader linkage, wherein said mirrored spreader linkage belongs to a class of spreader linkages which spread said tension springs, wherein the force curve for the loading of said spreader linkages first increases and then bends over to eventually go to zero at full spreading when the links of said spreader linkage become aligned, wherein this linkage spreading loading qualifies said first enhanced fully optimal spring system as a said enhanced fully optimal spring system, one or more parallel auxiliary springs, and one or more series auxiliary springs, wherein said parallel auxiliary springs act in parallel and in combination with monolithic mirrored arches to increase the combined force curve to become approximately constant as full compression is approached, wherein each of said monolithic mirrored arches further comprises a monolithic arch hinge which is a necked-down living hinge and which pivotally connects the top half of said monolithic mirrored arch to its mirrored image bottom half, wherein said mirrored spreader linkage further comprises on the top and on the bottom center links, mostly vertical links, and impinger links, wherein said center links are pivotally connected to said mostly vertical links by monolithic corner hinges, where said mostly vertical links are pivotally connected to said impinger links by monolithic impinger hinges, wherein said series auxiliary springs are positioned between said center links and the centers of said top half and said bottom half of said monolithic mirrored arches, wherein said parallel auxiliary springs are positioned between the opposing said center links of said internal linkage mirrored arch spring, wherein both said series auxiliary springs and said parallel auxiliary springs may be positioned in pairs spaced horizontally away from each other to provide a restoring force to keep said center links horizontal during compression, wherein said impinger links push outward against said monolithic arch hinges to flatten said monolithic mirrored arches, wherein said series auxiliary springs control and moderate the initial spreading of said monolithic mirrored arch by said mirrored spreader linkage, wherein the linkage force curve of the vertical compression force on said monolithic mirrored arches is for the force that would be applied if there were no parallel auxiliary springs and it first increases and then bends over and goes to zero during compression, wherein the force of said parallel auxiliary springs increases as said linkage force curve decreases so as to make sum of these two force curves approximately constant, wherein this sum is called the first combined force curve which is for said first enhanced fully optimal spring system, wherein said first combined force curve meets the requirements of said enhanced fully optimal spring system, wherein said auxiliary springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height, wherein said monolithic mirrored arches optionally comprise one or more nested monolithic mirrored arches nested within each other, wherein the strength of said internal linkage mirrored arch spring is increased significantly by the addition of each additional nested monolithic mirrored arch since its thickness is decreased only slightly.
 9. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a second enhanced fully optimal spring system which is also called a link-spread curved spring system which comprises a link-spread curved spring and one or more second auxiliary springs, wherein said link-spread curved spring comprises a second spreader linkage which comprises two or three links, a second curved spring, and link hinges, wherein said links are pivotally connected by said link hinges one to the other and at either end to the ends of said second curved spring via spring hinges, wherein the top one of said links is called the top link and it connects to the next link by the top link hinge, wherein the total length of the links comprising said second spreader linkage equals the length of said second curved spring so that said link-spread curve spring can fully flatten at full compression, wherein said top link hinge contacts said top load surface at the contact compression distance, wherein said contact compression distance can be adjusted by changing the lengths of the links of said second spreader linkage, wherein said second auxiliary springs comprise both an above top link hinge partial spring located between said top link hinge and top load surface and an adjust spring located adjacent to said second spreader linkage so as to be loaded directly between said top load surface and said bottom load surface, wherein said above top link hinge partial spring controls and moderates the initial spreading of said second curved spring, wherein the force curve of the vertical compression force on said link-spread curved spring is called the second force curve and it first increases and then bends over and goes to zero during compression, wherein the force of said above top link hinge partial spring increases as said second force curve decreases so as to make the combined second force curve approximately constant, which meets the requirements of said enhanced fully optimal spring system, wherein said second auxiliary springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 10. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a third enhanced fully optimal spring system which comprises a combined monolithic tensioned mirrored curved spring which comprises a monolithic tensioned mirrored curved spring and one or more third auxiliary springs which are loaded directly by said top load surface and said bottom load surface at partial compression, wherein said monolithic tensioned mirrored curved spring comprises an external quad linkage which is oriented like a diamond and which further comprises four monolithic quad links monolithically at the top and bottom connected by monolithic vertical necked-down vertices and on the two sides by monolithic horizontal necked-down vertices and a double mirrored curly v-spring tension element which further comprises four monolithic tension curved springs each of which is monolithically connected to monolithic horizontal necked-down vertices via a side vertex connection and each of which curves up (or down) until it is approaching vertical to connect to its mirrored image at the center via said monolithic vertical necked-down vertices, wherein said monolithic horizontal necked-down vertex further optionally comprises a first necked restraint, a monolithic loop, and a retainer pin, wherein said monolithic loop is a monolithic continuation between said monolithic quad link and said side vertex connection and said retainer pin is inserted from the side through said monolithic loop, wherein said first necked restraint encloses said monolithic loop to reinforce it to withhold the considerable force exerted by said side vertex and said monolithic quad link via said monolithic horizontal necked-down vertex, wherein the third force curve for the vertical force needed to pull apart said double mirrored curly v-spring tension element first increases and then reduces to zero, wherein the vertical force imparted by said third auxiliary springs increases as said third force curve decreases so as to make the combined third force curve approximately constant which meets the requirements of said enhanced fully optimal spring system, wherein said third auxiliary springs are preferentially said mirrored arch springs in which case all elements of said combined monolithic tensioned mirrored curved spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 11. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a fourth enhanced fully optimal spring system which comprises a combined band tensioned linkage spring which comprises a band tensioned linkage spring and one or more fourth auxiliary springs, which are loaded directly by said top load surface and said bottom load surface at partial compression, wherein said band tensioned linkage comprises a quad linkage which is oriented like a diamond and which further comprises four quad links connected at the top and bottom by vertical hinges and on the two sides by horizontal hinges, a tension band with band end loops on either end, and a shaft, wherein both said band end loops and said quad links (near where they connect to said horizontal hinges) are slotted so as to interleave one through the other so that said shaft can be inserted through said horizontal hinges so as to connect said quad linkage to said tension band, wherein the fourth force curve for the vertical force needed to pull apart said tension band first increases and then reduces to zero, wherein the vertical force imparted by said fourth auxiliary springs increases as said fourth force curve decreases so as to make the combined fourth force curve approximately constant which meets the requirements of said enhanced fully optimal spring system, wherein said fourth auxiliary springs are preferentially said mirrored arch springs in which case all elements said combined band tensioned linkage spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 12. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a fifth enhanced partly optimal spring system which is called a monolithic tensioned mirrored arch spring which comprises an outer top-loaded arch spring comprising a top extended arch and a bottom extended arch each of which comprises an extended flat section at its center and an outer tip section where it connects to the other, an inner side-loaded arch spring on the top half which connects to said outer-tip section on either end via inner tip section and via inter-arch section, a pair of inner tension-loaded curly v-springs on the bottom half which connect to each other at the center via inter curly v-spring tip section and which connect to said outer-tip section on either end via said inner tip section and via said inter-arch section, and a pair of outer-tip spacers which space apart said outer-tip sections so that said outer top-loaded arch spring can fully flatten without interference with said inner side-loaded arch spring or said inner tension-loaded curly v-spring, wherein said outer-tip sections are clamped to said outer-tip spacer by outer clamps and said inner-tip sections are clamped to their mirrored image said inner-tip sections via said inner clamps, wherein both said inner side-loaded arch spring and said inner tension-loaded curly v-spring are equivalent as inner tension elements and can be substituted for the other but only said inner side-loaded arch spring is mentioned the further explanation here, wherein said inner side-loaded arch spring is located inside of and pulls on said outer top-loaded arch spring via said inter-arch section, wherein these three elements form a continuous monolithic structure and they are interconnected via necked-down living hinges, wherein the slope of the fifth force curve—for the vertical compression force needed both bend said outer top-loaded arch spring and to pull apart said inner side-loaded arch—decreases to approximately half of its initial value during the latter part of compression which meets the requirements of said enhanced partly optimal spring system, wherein all elements of said band tensioned linkage spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 13. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises a sixth enhanced partly optimal spring system which comprises a tensioned band mirrored arch spring which comprises a second tension band with second band end loops on either end, a pair of mirrored band arches each comprising a center arch section and arch tips which impinge their mirrored image arch tips via said second tension band, a second band retainer pin, and a pair of band pivots, wherein said second band retainer pin is slid from the side through said second band end loops so as to prevent second band end loops from sliding through said arch tips which are compressing said second tension band, wherein the slope of the sixth force curve—for the vertical compression force needed both bend said mirrored band arches and stretch said second tension band—decreases to approximately half of its initial value during the latter part of compression which meets the requirements of said enhanced partly optimal spring system, wherein all elements of said tensioned band mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 14. The optimized shoe of claim 9 wherein said link-spread curved spring system comprises a seventh enhanced fully optimal spring system which comprises a combined tensioned links rotating arms curved spring system which comprises a tensioned links rotating arms curved spring and a seventh auxiliary spring, wherein said tensioned links rotating arms curved spring comprises a top arm, a bottom arm, an arm hinge which connects said top arm and said bottom arm, and a pair of said link-spread curved springs which are mirrored images of each other to form a configuration analogous to said curly v-spring, wherein said seventh auxiliary spring is positioned between said top arm and said bottom arm so as to engage them when they are partially folded, wherein on one end said spring hinges hingeably connect to said top arm and said bottom arm at mirrored positions, wherein on the other end said spring hinges hingeably connect and impinge each other, wherein the pivotal connection of these said second curved springs is preferentially achieved by a curved arch pivot which is a necked-down living hinge, wherein when the mirrored ones of said top link hinges impinge each other by the loaded folding of said top arm and said bottom arm about said arm hinge, the mirrored said spreader linkages straighten the mirrored said second curved springs, wherein the torque curve of said loaded folding is called the first torque curve and it first increases and then bends over and goes to zero during said loaded folding, wherein the torque exerted by said seventh auxiliary spring to resist said loaded folding increases as said torque curve decreases so as to make the combined torque curve approximately constant, which meets the requirements of said enhanced fully optimal spring system, wherein said seventh auxiliary spring is preferentially said curly v-spring in which case all elements of said combined tensioned links rotating arms curved spring system flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 15. The optimized shoe of claim 7 wherein said enhanced optimal spring system comprises an eighth enhanced partly optimal spring system which comprises an end-refined curved spring which comprises a solid initial section and a stiffness-changing rotating end section, wherein said solid initial section is oriented at its base primarily horizontally and said solid initial section curves upward for a solid portion of said elemental spring height to rigidly or monolithically attach to said stiffness-changing rotating end section, wherein said curved end-refined curved spring is loaded at its bottom by said bottom load surface and at its top by said top load surface which freely translates horizontally with respect to said bottom load surface, wherein during the initial portion of said spring compression the spring deflection is primarily due to the flattening of said solid initial section, wherein during the latter portion of said spring compression said spring deflection is primarily due to the compression and flattening of said stiffness-changing rotating end section as it rotates, wherein the stiffness of said stiffness-changing rotating end section can be independently parameterized to be weaker, wherein the force curve for compression of said end-refined curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section, after which said force curve bends over to become softer, which meets the requirements of said enhanced partly optimal spring system.
 16. The optimized shoe of claim 15 wherein said end-refined spring system comprises a ninth enhanced partly optimal spring system which comprises a kite end curved spring, wherein said stiffness-changing rotating end section comprises a kite end section which splits (at the lower vertex) partway up said solid initial section into two kite arch arms which rejoin at the kite top end at the upper vertex at the top of said elemental spring height to form a kite arm mirrored arch which is eventually closed to flatten when the kite arm centers of said kite arms are directly loaded along the kite center line between the centers of the two said kite arms, wherein said kite end section has a vertex axis between said lower vertex and said upper vertex, wherein said vertex axis is oriented primarily vertically (although it might be somewhat diagonal) at the beginning of said spring compression, wherein said vertex axis rotates to be fully horizontal at the end of said spring compression, wherein the stiffness to bending of said kite end section is sufficient so that its bends only slightly or not at all during said initial portion of said spring compression, wherein said kite end section compresses during the latter portion of compression as said vertex axis rotates so that said kite end becomes more directly loaded along said kite line center so that the force required to compress said kite end section is reduced, wherein the force curve for compression of said kite end curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section while the force curve during the latter part of compression is primarily due to the compression of said kite end section which can be independently parameterized to be weaker so that in the latter part of compression the force curve bends over to become softer which meets the requirements of said enhanced partly optimal spring system, wherein said kite end curved spring can also be used to construct said set of arch spring configurations such as for said curly v-spring—in like manner to how they were constructed for said elemental curved spring.
 17. The optimized shoe of claim 15 wherein end-refined spring comprises a tenth enhanced partly optimal spring system which comprises an arrow head curved spring, wherein said stiffness-changing rotating end section comprises an arrow head end section comprising a rigid end rigidly attached to said solid initial section and an arrow curved spring the end of which is fixably attached to the tip end of said rigid end, wherein said arrow head curved spring is parallel to said rigid end at its attachment point, wherein said arrow head curved spring curves away from said rigid end as it extends to its arrow end, wherein said arrow head curved spring can be on one or both sides of said rigid end, wherein said arrow head curved spring is not in contact with its adjacent load surface at the beginning of spring compression but its tip end impinges its adjacent load surface during the latter portion of said spring compression so that said arrow head curved spring is completely compressed and flattened against said rigid end at full compression when said rigid end has rotated to be horizontal, wherein the force curve for compression of said arrow curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section while the force curve during the latter part of compression is primarily due to the compression of said arrow head end section which can be independently parameterized to be weaker so that in the latter part of compression the force curve bends over to become softer which meets the requirements of said enhanced partly optimal spring system, wherein said arrow head curved spring can be used to construct said set of arch spring configurations such as for said curly v-spring—in like manner to how they were constructed for said elemental curved spring.
 18. The optimized shoe of claim 7 wherein said enhanced optimal spring systems are configured to be in a multi-sided configuration in which there are one or more sides, wherein each side is preferentially wedge shaped to maximize the spring force.
 19. The optimized shoe of claim 1 wherein said heel-pop mechanism comprises a generic parallelogram-like structure which further comprises a p-structure which comprises four p-elements which comprise said footplate as the A-top, said groundplate as the p-bottom, a p-front as the generic front side, a p-rear as the generic rear side, wherein said p-elements are pivotally interconnected via p-pivots, wherein said toe section comprises a toe plate, wherein said heel-pop mechanism functions as follows, wherein during the beginning of said heel-lift period the weight of said user holds down said toe plate which holds down said p-front even while said optimized spring system acts to p-expand said p-structure, wherein this p-expansion acts to lift the heel of said user upward by an enhanced distance substantially greater than the compression distance of the said heel section during said compression period, wherein the goal of said heel-pop mechanism is achieved.
 20. The optimized shoe of claim 19 wherein said compressible sole comprises an anti-toe-sink mechanism which prevents said toe plate from further sinking during toe-off for the case when said compressible sole only partially compresses during said compression period.
 21. The optimized shoe of claim 20 wherein said anti-toe-sink mechanism comprises a toe parallelogram, a ladder stop, a toe stop on the bottom of said toe plate on either side, and a toe spring, wherein said toe parallelogram comprises said a top toe link on the top side, a front toe link on the front side, a rear toe link on the rear side, and a bottom toe link on the bottom side, wherein said ladder stop also features ladder steps on its front side, wherein the shape of said ladder steps follows a path parallel to the track of said toe hinge during compression (forward and downward), wherein said anti-toe-sink mechanism functions as follows, during compression of said compressible sole, said toe spring weakly biases said toe plate to stay above said top toe link until said user weights said toe plate just before the beginning said heel-lift period at which time said toe stop impinges the nearest said ladder step thereby preventing toe sink, wherein this prevention can occur at any and all levels of partial compression of said compressible sole, wherein said user is also free to run on his or hers or its toes without undue toe sink.
 22. The optimized shoe of claim 21 wherein said heel-pop shoe comprises a linkage-spread curved spring heel-pop shoe which comprises a monolithic generic parallelogram-like structure, a monolithic generic toe parallelogram-like structure, said anti-toe-sink structure, and one or more auxiliary p-springs, wherein said monolithic generic parallelogram-like structure comprises a front double link-spread spring for said p-front which can optionally be a p-tension band, a rear double link-spread spring for said p-rear which can optionally be a p-tension band, a mid footplate link for said p-top, a groundplate link for said p-bottom, and an end footplate link, wherein all just said links interconnect via monolithic, necked-down living hinges call mono pivots, wherein each said double link-spread spring comprises said double linkage and said curved spring, wherein said auxiliary p-springs comprise firstly one or more said above top link hinge partial springs located between said top link hinge and said top load surface and they comprise secondly one or more said adjust springs located adjacent to said front and rear spreader linkages so as to be loaded directly between said top load surface and said bottom load surface, wherein said above top link hinge partial springs control and moderate the initial spreading of said curved spring, wherein the force curve of the vertical compression force on the link-spread said curved spring is called the p-force curve and it first increases and then bends over and goes to zero during compression, wherein the force of said above top link hinge partial spring increases as said p-force curve decreases so as to make the combined p-force curve approximately constant, which meets the requirements of said enhanced optimal spring system, wherein said second auxiliary p-springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height, wherein said monolithic generic toe parallelogram-like structure comprises a front footplate link, a toe curved spring, a spring plate on the bottom, and a rear toe curved spring which is one and the same as said curved spring of said front double link-spread spring so this is the shared p-element between said monolithic generic parallelogram-like structure and said monolithic generic toe parallelogram-like structure—as this sharing is what makes possible said enhanced heel-lift, wherein the purpose of said monolithic generic toe parallelogram-like structure is to maintain said front footplate link approximately horizontal during compression so that said toe stop does not rotate downward to engage on of said ladder steps until said user pushes her toe down just before said heel-lift begins, wherein said toe curved spring is only just strong enough to maintain said front footplate link so that the maximum said impact energy is stored in said front double link-spread spring, said rear double link-spread spring, and said auxiliary p-springs, which act as said spring system—the combined energy of which provides said enhanced heel-lift, wherein the p-front and p-rear elements of said monolithic generic toe parallelogram-like structure feature curved springs which act as the structural links as well as spring elements to combine functions, wherein there is some seesaw rocking of said compressible sole, but this is sufficiently negligible as compared with the advantage of eliminating the need for a separate parallelogram in addition to the spring system.
 23. The optimized shoe of claim 22 wherein said heel-pop shoe comprises a curved spring heel-pop shoe which comprises a monolithic generic parallelogram-like structure, a monolithic generic toe parallelogram-like structure, and said anti-toe-sink structure, wherein said monolithic generic parallelogram-like structure comprises a front curved spring for said p-front, a rear curved spring for said p-rear, a mid footplate link which serves as said p-top and which features an extension further rearward of said p-pivot for the connection between the top of said rear curved spring and said mid footplate link, and a groundplate link for said p-bottom, wherein said p-pivots for the connections between said groundplate link and both said front curved spring and said rear curved spring are simply merged monolithic pivots in which said front curved spring and said rear curved spring curves become horizontal to merge with said groundplate link, wherein the same merged monolithic pivots are used for the connections between front curved spring and said rear curved spring and said footplate link, wherein conventional cylindrical hinges with shafts and bearings can also be used for these connections to said footplate link, wherein said monolithic generic toe parallelogram-like structure comprises said curved spring parallelogram-like structure, wherein the c-force curve of said curved spring heel-pop shoe is linear.
 24. The optimized shoe of claim 22 wherein said heel-pop shoe comprises a parallelogram heel-pop shoe which comprises a monolithic parallelogram structure, a monolithic toe parallelogram structure, said anti-toe-sink structure, wherein said monolithic generic parallelogram-like structure comprises a front mono link for said p-front, a rear mono link for said p-rear, said footplate link which serves as said p-top and which features an extension further rearward of said p-pivot (which provides the connection between the top of said rear curved spring and said mid footplate link), and said groundplate link for said p-bottom, wherein said p-pivots for the connections between said groundplate link and said front mono link and said rear mono link are simply merged monolithic pivots in which said front mono link and said rear mono link necks down and curves (close to their ends) to become horizontal to merge with said groundplate link and likewise for the connections to said footplate, wherein conventional cylindrical hinges with shafts and bearings can also be used for all these merged monolithic pivots, wherein said monolithic generic toe parallelogram-like structure comprises bottom toe link, front toe link, top toe link, and rear toe link (which is one and the same as said front mono link), wherein the sharing of this link is the requirement for said enhanced heel-lift, wherein monolithic pivots are preferentially used for all connections of the links of said parallelogram heel-pop shoe although conventional cylindrical hinges with shafts and bearings can be used as well, wherein said conventional cylindrical hinges guarantee that there is no seesawing of said compressible sole as the foot impact moves from the heel to the toe of said use, wherein said spring system comprises one or more of any said enhanced arch springs, which allow said top load surface to translate horizontally with respect to said bottom load surface, which can be used to achieve a linear force curve such as said rolling mirrored arch spring or said curly v-spring, wherein said spring system comprises one or more of any such said enhanced optimal springs—which allow said top load surface to translate horizontally with respect to said bottom load surface and which can be used to achieve an optimal force curve, wherein these enhanced optimal springs include a rolling version of said internal linkage mirrored arch spring, said combined monolithic tensioned mirrored curved spring, said combined band tensioned linkage spring, a rolling version of said combined monolithic tensioned mirrored arch spring and a rolling version of said combined tensioned band mirrored arch spring, wherein rolling version means that such a spring starts tilted (rotated) back and then tilts forward during compression so that it is symmetrical oriented and fully flattened at full compression.
 25. An optimal spring system, which comprises a set of enhanced optimal arch springs further comprising a set of enhanced arch springs each of which is constructed from one or more arch spring types, and a fiberglass composite construction, wherein said optimal spring system has a optimal force curve, wherein the force-curve optimization goal for said optimal force curve is to maximize the amount of energy absorbed (namely the area under the force curve) for a given said maximum force point, wherein one way to achieve a said optimal force curve is to vary the spring structure and shape so as to achieve a softer force curve, wherein said set of enhanced arch springs becomes said set of enhanced optimal arch springs when they have said optimal forces curves, wherein fiberglass composite is the significantly preferred material for the resilient spring elements of said enhanced arch springs because it has a very low mechanical hysteresis loss of approximately one to two percent as compared to approximately 20-50% for injection moldable materials such as thermoplastic polyurethanes (for example, pellethane 2363 or PEBAX 5533), wherein any other material with critical parameters for flexibility and bending strength which are similar to those of fiberglass can also be used, wherein the critical parameter for flexibility for said arch springs is the elongation limit of the fiber or of the geometrical construction of the fiber, wherein each said arch spring type represents a combination of elemental curved springs in different orientations, wherein said elemental curved spring is also called a curved arm and it is a curved spring which substantially flattens to a flat plate under full compression, wherein the end of said curved arm (which is horizontal and approximately parallel to the adjacent base load surface) is called the base end and the end of said curved arm that is approximately perpendicular to or diagonal with respect to the adjacent tip load surface is the tip end, wherein the full compression thickness at full compression of said elemental curved spring is the thickness of said curved arm, wherein the approximate shape of said elemental curved spring is a quarter of a circle, wherein the elemental spring height of said elemental curved spring is approximately the radius of said quarter of a circle, wherein said elemental full compression thickness is substantially smaller than the elemental spring height possibly by a factor of ten to twenty, wherein the first arch spring type is simply said elemental curved spring, wherein said tip load surface freely translates horizontally with respect to base load surface said elemental curved spring, wherein the spring strength comparisons for said elemental curved spring are as follows, wherein the spring strength using fiberglass composite is approximately ten times stronger than the spring strength using carbon fiber, wherein the spring strength using fiberglass composite is approximately sixteen times stronger than the spring strength using said injection moldable materials, wherein the spring weight using fiberglass composite is approximately twelve times lighter than the spring weight using carbon fiber composite, wherein the spring weight for fiberglass composite is approximately eight times lighter than the spring weight using said injection moldable materials.
 26. The optimal spring system of claim 25 wherein said enhanced optimal arch springs are pre-loaded to improve said optimal force curve, wherein the force at the beginning of the optimal spring compression is a predetermined value (for example one-third the force value at full spring compression), wherein the work done by said spring system is the area under the curve of the force versus the spring deflection, wherein said work is absorbed with a reduced value of the maximum force value point as compared with the maximum force value point when there is no pre-load, wherein this improvement applies for both said optimal force curve and for a linear force curve, wherein the improvement due to pre-load is independent of the improvement due to a constant force curve so either improvement applies to said optimal force curve and the combination of both improvements also applies to said optimal force curve, wherein said pre-load is accomplished with a physical restraint such as a tether or such as a structural restraint, wherein the first criterion for said optimal spring system is to pre-load said optimal spring system, and the second criterion for said optimal spring system is to create a geometry so that the slope of said optimal force curve decreases or even becomes approximately constant throughout the latter said sole compression.
 27. The optimal spring system of claim 26 wherein said optimal spring system comprises a set of enhanced arch springs each of which is constructed from one or more arch spring types, wherein each said arch spring type represents a combination of elemental curved springs in different orientations, wherein said elemental curved spring is also called a curved arm and it is a curved spring which substantially flattens to a flat plate under full compression, wherein the first arch spring type is said elemental curved spring, wherein the end of said curved arm (which is horizontal and approximately parallel to the adjacent base load surface) is called the base end and the end of said curved arm that is approximately perpendicular to or diagonal with respect to the adjacent tip load surface is the tip end, wherein the full compression thickness at full compression of said elemental curved spring is the thickness of said curved arm, wherein the approximate shape of said elemental curved spring is a quarter of a circle although the curvature may be somewhat different, wherein the elemental spring height of said elemental curved spring is approximately the radius of said quarter of a circle, wherein said elemental full compression thickness is substantially smaller than the elemental spring height possible by a factor of ten to twenty, wherein the first arch spring type is simply said elemental curved spring, wherein said tip end load surface freely translates horizontally with respect to said base load surface, wherein the spring strength comparisons for said elemental curved spring are as follows, wherein the spring strength using fiberglass composite is approximately ten times stronger than the spring strength using carbon fiber, wherein the spring strength using fiberglass composite is approximately sixteen times stronger than the spring strength using said injection moldable materials, wherein the spring weight using fiberglass composite is approximately twelve times lighter than the spring weight using carbon fiber composite, wherein the spring weight for fiberglass composite is approximately eight times lighter than the spring weight using said injection moldable materials.
 28. The optimal spring system of claim 27 wherein said optimal spring system comprises one of more said arch spring types, wherein the second said arch spring type is called an arch spring in which two said elemental curved springs are combined to form the shape of an arch, wherein the left side of said elemental curved spring is the mirror image of the right side of said elemental curved spring constructed about the vertical line at the junction of the opposing said base ends, wherein the arch center is located where the base ends of the opposing said elemental curved springs join, wherein the third said arch spring type is called a mirrored arch spring in which case the upper concave downward said arch spring is mirrored about the horizontal line just below the opposing said tip ends of the upper said arch spring, wherein the said arch centers of the upper and lower said arch springs are loaded by their adjacent mirrored load surfaces causing the opposing said tip ends to move outward horizontally as said mirrored arch spring fully flattens, wherein said mirrored load surfaces do not translate horizontally with respect each other and instead they move vertically and directly toward each other during said spring compression, wherein the fourth said arch spring type is called a rolling mirrored arch spring in which case the top and bottom of said mirrored arch springs have a circular shape in which case said rolling mirrored arch spring can roll somewhat as it is being loaded by two surfaces which are translating horizontally with respect to one another, wherein the fifth said arch spring type is called a half mirrored arch spring in which case said mirrored arch spring is cut in half along a vertical line though its center when viewed from the side, wherein the sixth said arch spring type is called a curly v-spring in which case said elemental curved spring is combined with its mirrored image also called an inverted said elemental curved spring to form said curly v-spring which looks like the letter V turned on its side with each of its arms being curled in the shape of an elemental curved spring, wherein the seventh said arch spring type is called nested arch springs in which one or more said arch spring types is or are nested within another arch spring type to form a nested arch spring at one or more levels of nesting, wherein the base of said elemental arch springs are offset in the vertical direction with respect to each other so that when said nested arch spring fully compresses, each component said elemental curved spring is approximately horizontal along its entire length, wherein the total spring strength of said nested arch spring is increased over that of a single said arch spring albeit at the cost of an increase in the thickness of said nest arch spring at full compression, wherein all above said arch spring types and more complex variations made from them have similar force curves and behaviors to the force curves of said elemental curved springs of which they are constructed.
 29. The optimal spring system of claim 28 wherein said arch spring types comprise spring elements, linkage elements, and hinges, wherein said spring elements and said linkage elements are connected to each other with hinges, wherein one or more said hinges are conventional cylindrical hinges comprising shafts and bearings.
 30. The optimal spring system of claim 26 which comprises an enhanced optimal spring system which is constructed of said arch spring types, wherein said enhanced optimal spring system is designed to optimize the force curve for devices such as footwear where it is advantageous to minimize the maximum force point along the force curve (especially when there is an impact force) on said user, on the structural elements of said spring system and on the device within it is incorporated, wherein the force-curve optimization goal for said force curve optimized spring is to maximum the amount of energy absorbed (namely the area under the force curve) for a given said maximum force point, wherein the first part of a method to achieve a desired optimized force curve is to pre-load it and the second part is to vary the spring structure and shape so as to achieve a softer, more constant force curve, wherein these changes in force curve can reduce said maximum force value by 25% to approximately 40% as compared to a spring system with a linear force curve, wherein there are two classes of enhanced optimal spring systems, namely an enhanced fully optimal spring system where the force curve becomes approximately constant during the latter part of compression and namely an enhanced partly optimal spring system where the slope of the force curve decreases to approximately half of its initial value during the latter part of compression, wherein when a non-linear finite element analysis is done to determine the maximum allowable thickness (and hence the maximum possible force) of said curved arms within the stress limits of the material of which said curved arms are made, the total energy absorbed (work done) per unit area by each said arch spring is linearly proportional to the full deflection value which is the deflection at full compression so that it is easy to achieve a particular total energy absorbed by simply choosing the corresponding said full deflection value, which means that the only way to change said total energy absorbed (work done) per unit area is to change said full deflection value, wherein the impact energy of running is absorbed by the compression of said compressible sole with the sole compression energy and by the compression of the leg of said user with the leg compression energy, wherein the third criterion for optimization of said sole compression energy is to determine the optimal sole compression energy by experiment and then to realize said optimal sole compression energy by choosing the corresponding particular said deflection value, wherein one or more said hinges are necked-down living hinges which permit a continuous monolithic construction between adjacent ones of said linkages elements and said spring elements.
 31. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises first enhanced fully optimal spring system which is also called an internal linkage mirrored arch spring system which comprises monolithic mirrored arches, wherein said monolithic mirrored arches belong to a tension spring class of tensioned springs which comprise said elemental curved springs and tension band springs, mirrored spreader linkage, wherein said mirrored spreader linkage belongs to a class of spreader linkages which spread said tension springs, wherein the force curve for the loading of said spreader linkages first increases and then bends over to eventually go to zero at full spreading when the links of said spreader linkage become aligned, wherein this linkage spreading loading qualifies said first enhanced fully optimal spring system as a said enhanced fully optimal spring system, one or more parallel auxiliary springs, and one or more series auxiliary springs, wherein said parallel auxiliary springs act in parallel and in combination with monolithic mirrored arches to increase the combined force curve to become approximately constant as full compression is approached, wherein each of said monolithic mirrored arches further comprises a monolithic arch hinge which is a necked-down living hinge and which pivotally connects the top half of said monolithic mirrored arch to its mirrored image bottom half, wherein said mirrored spreader linkage further comprises on the top and on the bottom center links, mostly vertical links, and impinger links, wherein said center links are pivotally connected to said mostly vertical links by monolithic corner hinges, where said mostly vertical links are pivotally connected to said impinger links by monolithic impinger hinges, wherein said series auxiliary springs are positioned between said center links and the centers of said top half and said bottom half of said monolithic mirrored arches, wherein said parallel auxiliary springs are positioned between the opposing said center links of said internal linkage mirrored arch spring, wherein both said series auxiliary springs and said parallel auxiliary springs may be positioned in pairs spaced horizontally away from each other to provide a restoring force to keep said center links horizontal during compression, wherein said impinger links push outward against said monolithic arch hinges to flatten said monolithic mirrored arches, wherein said series auxiliary springs control and moderate the initial spreading of said monolithic mirrored arch by said mirrored spreader linkage, wherein the linkage force curve of the vertical compression force on said monolithic mirrored arches is for the force that would be applied if there were no parallel auxiliary springs and it first increases and then bends over and goes to zero during compression, wherein the force of said parallel auxiliary springs increases as said linkage force curve decreases so as to make sum of these two force curves approximately constant, wherein this sum is called the first combined force curve which is for said first enhanced fully optimal spring system, wherein said first combined force curve meets the requirements of said enhanced fully optimal spring system, wherein said auxiliary springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height, wherein said monolithic mirrored arches optionally comprise one or more nested monolithic mirrored arches nested within each other, wherein the strength of said internal linkage mirrored arch spring is increased significantly by the addition of each additional nested monolithic mirrored arch since its thickness is decreased only slightly.
 32. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a second enhanced fully optimal spring system which is also called a link-spread curved spring system which comprises a link-spread curved spring and one or more second auxiliary springs, wherein said link-spread curved spring comprises a second spreader linkage which comprises two or three links, a second curved spring, and link hinges, wherein said links are pivotally connected by said link hinges one to the other and at either end to the ends of said second curved spring via spring hinges, wherein the top one of said links is called the top link and it connects to the next link by the top link hinge, wherein the total length of the links comprising said second spreader linkage equals the length of said second curved spring so that said link-spread curve spring can fully flatten at full compression, wherein said top link hinge contacts said top load surface at the contact compression distance, wherein said contact compression distance can be adjusted by changing the lengths of the links of said second spreader linkage, wherein said second auxiliary springs comprise both an above top link hinge partial spring located between said top link hinge and top load surface and an adjust spring located adjacent to said second spreader linkage so as to be loaded directly between said top load surface and said bottom load surface, wherein said above top link hinge partial spring controls and moderates the initial spreading of said second curved spring, wherein the force curve of the vertical compression force on said link-spread curved spring is called the second force curve and it first increases and then bends over and goes to zero during compression, wherein the force of said above top link hinge partial spring increases as said second force curve decreases so as to make the combined second force curve approximately constant, which meets the requirements of said enhanced fully optimal spring system, wherein said second auxiliary springs are preferentially said curly v-springs in which case all elements of said internal linkage mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 33. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a third enhanced fully optimal spring system which comprises a combined monolithic tensioned mirrored curved spring which comprises a monolithic tensioned mirrored curved spring and one or more third auxiliary springs which are loaded directly by said top load surface and said bottom load surface at partial compression, wherein said monolithic tensioned mirrored curved spring comprises an external quad linkage which is oriented like a diamond and which further comprises four monolithic quad links monolithically at the top and bottom connected by monolithic vertical necked-down vertices and on the two sides by monolithic horizontal necked-down vertices and a double mirrored curly v-spring tension element which further comprises four monolithic tension curved springs each of which is monolithically connected to monolithic horizontal necked-down vertices via a side vertex connection and each of which curves up (or down) until it is approaching vertical to connect to its mirrored image at the center via said monolithic vertical necked-down vertices, wherein said monolithic horizontal necked-down vertex further optionally comprises a first necked restraint, a monolithic loop, and a retainer pin, wherein said monolithic loop is a monolithic continuation between said monolithic quad link and said side vertex connection and said retainer pin is inserted from the side through said monolithic loop, wherein said first necked restraint encloses said monolithic loop to reinforce it to withhold the considerable force exerted by said side vertex and said monolithic quad link via said monolithic horizontal necked-down vertex, wherein the third force curve for the vertical force needed to pull apart said double mirrored curly v-spring tension element first increases and then reduces to zero, wherein the vertical force imparted by said third auxiliary springs increases as said third force curve decreases so as to make the combined third force curve approximately constant which meets the requirements of said enhanced fully optimal spring system, wherein said third auxiliary springs are preferentially said mirrored arch springs in which case all elements of said combined monolithic tensioned mirrored curved spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 34. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a fourth enhanced fully optimal spring system which comprises a combined band tensioned linkage spring which comprises a band tensioned linkage spring and one or more fourth auxiliary springs, which are loaded directly by said top load surface and said bottom load surface at partial compression, wherein said band tensioned linkage comprises a quad linkage which is oriented like a diamond and which further comprises four quad links connected at the top and bottom by vertical hinges and on the two sides by horizontal hinges, a tension band with band end loops on either end, and a shaft, wherein both said band end loops and said quad links (near where they connect to said horizontal hinges) are slotted so as to interleave one through the other so that said shaft can be inserted through said horizontal hinges so as to connect said quad linkage to said tension band, wherein the fourth force curve for the vertical force needed to pull apart said tension band first increases and then reduces to zero, wherein the vertical force imparted by said fourth auxiliary springs increases as said fourth force curve decreases so as to make the combined fourth force curve approximately constant which meets the requirements of said enhanced fully optimal spring system, wherein said fourth auxiliary springs are preferentially said mirrored arch springs in which case all elements said combined band tensioned linkage spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 35. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a fifth enhanced partly optimal spring system which is called a monolithic tensioned mirrored arch spring which comprises an outer top-loaded arch spring comprising a top extended arch and a bottom extended arch each of which comprises an extended flat section at its center and an outer tip section where it connects to the other, an inner side-loaded arch spring on the top half which connects to said outer-tip section on either end via inner tip section and via inter-arch section, a pair of inner tension-loaded curly v-springs on the bottom half which connect to each other at the center via inter curly v-spring tip section and which connect to said outer-tip section on either end via said inner tip section and via said inter-arch section, and a pair of outer-tip spacers which space apart said outer-tip sections so that said outer top-loaded arch spring can fully flatten without interference with said inner side-loaded arch spring or said inner tension-loaded curly v-spring, wherein said outer-tip sections are clamped to said outer-tip spacer by outer clamps and said inner-tip sections are clamped to their mirrored image said inner-tip sections via said inner clamps, wherein both said inner side-loaded arch spring and said inner tension-loaded curly v-spring are equivalent as inner tension elements and can be substituted for the other but only said inner side-loaded arch spring is mentioned the further explanation here, wherein said inner side-loaded arch spring is located inside of and pulls on said outer top-loaded arch spring via said inter-arch section, wherein these three elements form a continuous monolithic structure and they are interconnected via necked-down living hinges, wherein the slope of the fifth force curve—for the vertical compression force needed both bend said outer top-loaded arch spring and to pull apart said inner side-loaded arch—decreases to approximately half of its initial value during the latter part of compression which meets the requirements of said enhanced partly optimal spring system, wherein all elements of said band tensioned linkage spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 36. The optimal spring system of claim 30 wherein said enhanced optimal spring system comprises a sixth enhanced partly optimal spring system which comprises a tensioned band mirrored arch spring which comprises a second tension band with second band end loops on either end, a pair of mirrored band arches each comprising a center arch section and arch tips which impinge their mirrored image arch tips via said second tension band, a second band retainer pin, and a pair of band pivots, wherein said second band retainer pin is slid from the side through said second band end loops so as to prevent second band end loops from sliding through said arch tips which are compressing said second tension band, wherein the slope of the sixth force curve—for the vertical compression force needed both bend said mirrored band arches and stretch said second tension band—decreases to approximately half of its initial value during the latter part of compression which meets the requirements of said enhanced partly optimal spring system, wherein all elements of said tensioned band mirrored arch spring flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 37. The optimal spring system of claim 32 wherein said link-spread curved spring system comprises a seventh enhanced fully optimal spring system which comprises a combined tensioned links rotating arms curved spring system which comprises a tensioned links rotating arms curved spring and a seventh auxiliary spring, wherein said tensioned links rotating arms curved spring comprises a top arm, a bottom arm, an arm hinge which connects said top arm and said bottom arm, and a pair of said link-spread curved springs which are mirrored images of each other to form a configuration analogous to said curly v-spring, wherein said seventh auxiliary spring is positioned between said top arm and said bottom arm so as to engage them when they are partially folded, wherein on one end said spring hinges hingeably connect to said top arm and said bottom arm at mirrored positions, wherein on the other end said spring hinges hingeably connect and impinge each other, wherein the pivotal connection of these said second curved springs is preferentially achieved by a curved arch pivot which is a necked-down living hinge, wherein when the mirrored ones of said top link hinges impinge each other by the loaded folding of said top arm and said bottom arm about said arm hinge, the mirrored said spreader linkages straighten the mirrored said second curved springs, wherein the torque curve of said loaded folding is called the first torque curve and it first increases and then bends over and goes to zero during said loaded folding, wherein the torque exerted by said seventh auxiliary spring to resist said loaded folding increases as said torque curve decreases so as to make the combined torque curve approximately constant, which meets the requirements of said enhanced fully optimal spring system, wherein said seventh auxiliary spring is preferentially said curly v-spring in which case all elements of said combined tensioned links rotating arms curved spring system flatten at full compression to maximize the compression ratio of its initial height to its fully compressed height.
 38. The optimal spring system of claim 30 said enhanced optimal spring system comprises an eighth enhanced partly optimal spring system which comprises an end-refined curved spring which comprises a solid initial section and a stiffness-changing rotating end section, wherein said solid initial section is oriented at its base primarily horizontally and said solid initial section curves upward for a solid portion of said elemental spring height to rigidly or monolithically attach to said stiffness-changing rotating end section, wherein said curved end-refined curved spring is loaded at its bottom by said bottom load surface and at its top by said top load surface which freely translates horizontally with respect to said bottom load surface, wherein during the initial portion of said spring compression the spring deflection is primarily due to the flattening of said solid initial section, wherein during the latter portion of said spring compression said spring deflection is primarily due to the compression and flattening of said stiffness-changing rotating end section as it rotates, wherein the stiffness of said stiffness-changing rotating end section can be independently parameterized to be weaker, wherein the force curve for compression of said end-refined curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section, after which said force curve bends over to become softer, which meets the requirements of said enhanced partly optimal spring system.
 39. The optimal spring system of claim 38 wherein said end-refined spring system comprises a ninth enhanced partly optimal spring system which comprises a kite end curved spring, wherein said stiffness-changing rotating end section comprises a kite end section which splits (at the lower vertex) partway up said solid initial section into two kite arch arms which rejoin at the kite top end at the upper vertex at the top of said elemental spring height to form a kite arm mirrored arch which is eventually closed to flatten when the kite arm centers of said kite arms are directly loaded along the kite center line between the centers of the two said kite arms, wherein said kite end section has a vertex axis between said lower vertex and said upper vertex, wherein said vertex axis is oriented primarily vertically (although it might be somewhat diagonal) at the beginning of said spring compression, wherein said vertex axis rotates to be fully horizontal at the end of said spring compression, wherein the stiffness to bending of said kite end section is sufficient so that its bends only slightly or not at all during said initial portion of said spring compression, wherein said kite end section compresses during the latter portion of compression as said vertex axis rotates so that said kite end becomes more directly loaded along said kite line center so that the force required to compress said kite end section is reduced, wherein the force curve for compression of said kite end curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section while the force curve during the latter part of compression is primarily due to the compression of said kite end section which can be independently parameterized to be weaker so that in the latter part of compression the force curve bends over to become softer which meets the requirements of said enhanced partly optimal spring system, wherein said kite end curved spring can also be used to construct said set of arch spring configurations such as for said curly v-spring—in like manner to how they were constructed for said elemental curved spring.
 40. The optimal spring system of claim 38 wherein end-refined spring comprises a tenth enhanced partly optimal spring system which comprises an arrow head curved spring, wherein said stiffness-changing rotating end section comprises an arrow head end section comprising a rigid end rigidly attached to said solid initial section and an arrow curved spring the end of which is fixably attached to the tip end of said rigid end, wherein said arrow head curved spring is parallel to said rigid end at its attachment point, wherein said arrow head curved spring curves away from said rigid end as it extends to its arrow end, wherein said arrow head curved spring can be on one or both sides of said rigid end, wherein said arrow head curved spring is not in contact with its adjacent load surface at the beginning of spring compression but its tip end impinges its adjacent load surface during the latter portion of said spring compression so that said arrow head curved spring is completely compressed and flattened against said rigid end at full compression when said rigid end has rotated to be horizontal, wherein the force curve for compression of said arrow curved spring increases rapidly during said initial portion of spring compression primarily due to the flattening of said solid initial section while the force curve during the latter part of compression is primarily due to the compression of said arrow head end section which can be independently parameterized to be weaker so that in the latter part of compression the force curve bends over to become softer which meets the requirements of said enhanced partly optimal spring system, wherein said arrow head curved spring can be used to construct said set of arch spring configurations such as for said curly v-spring—in like manner to how they were constructed for said elemental curved spring.
 41. The optimal spring system of claim 30 wherein said enhanced optimal spring systems are configured to be in a multi-sided configuration in which there are one or more sides, wherein each side is preferentially wedge shaped to maximize the spring force.
 42. The optimal spring system of claim 25 wherein said optimal spring system comprises an optimized conventional shoe wherein said enhanced optimal spring systems are used in conventional shoes, meaning shoes that do not have a heel-pop mechanism also called an enhanced heel-lift mechanism to lift said heel section during said heel-lift period by a distance that is substantially greater than the distance over which said heel section is compressed during said compression period which is called herein enhanced heel-lift, wherein said heel-pop mechanism provides energy return that is substantially greater than that of conventional shoes which do not have said heel-pop mechanism, wherein the significance of said energy return is that the metabolic energy cost of running is substantially reduced, wherein said optimized conventional shoe comprises a compressible sole, a top load surface on the upper side of said compressible sole further comprising a footplate hingeably connected to a toe plate by a toe hinge, a bottom load surface called a groundplate on the lower side of said compressible sole, wherein said compressible sole further comprises a toe section, wherein said toe section preferentially incorporates a conventional toe stop to elevate the take-off surface during toe-off, a forefoot section, and a heel section, wherein said compressible sole further comprises a spring system which resists compression and which stores the impact energy of compression.
 43. The optimal spring system of claim 42 wherein the set of said enhanced optimal spring systems comprises a vertical compression subset, wherein said optimal spring system is loaded by said footplate against said groundplate, wherein for said vertical compression class of arch spring types said footplate does not translate horizontally with respect to said groundplate during the compression of said optimal spring system, wherein for said forward translating class of arch spring types said upper load surface does translate horizontally with respect to said lower load surface during the compression of said optimal spring system, wherein the following enhanced optimal spring systems belong to said vertical compression subset: said internal linkage mirrored arch spring, said combined monolithic tensioned mirrored curved spring, said combined band tensioned linkage spring, said monolithic tensioned mirrored arch spring, said tensioned band mirrored arch spring, and said end-refined curved spring in curly v-spring configuration.
 44. The optimal spring system of claim 43 wherein said spring system of said optimized conventional shoe comprises one or more members of said vertical compression subset of said enhanced optimal spring systems, wherein each said member is called an optimal shoe spring, wherein one or more said shoe springs may be located anywhere in said toe section, said forefoot section, or said heel section, wherein said optimal shoe springs may be oriented any way, wherein said optimal shoe springs may have small enough widths so as to be distributed across the width of said compressible sole, wherein said optimal shoe springs may be oriented at any angle, wherein the strength of said optimal shoe springs may vary across both the width and the length of said compressible sole, where said compressible sole may be of constant thickness or of tapered thickness, where said optimal shoe springs may be insertable or permanently attached.
 45. The optimal spring system of claim 25 wherein said optimal spring system comprises an optimal force curve method which further comprises a first means to determine both the user energy which is amount of impact energy absorbed by the legs and feet of said user and the sole energy which is the amount of impact energy absorbed by said compressible sole and a second means to adjust said sole energy so that its value increases while said user energy decreases for a given total impact energy absorbed which corresponds to a reduction in the metabolic energy for running, wherein for said arch spring types and said enhanced arch springs and said enhanced optimal arch springs, the maximum shoe energy per unit area that can be absorbed at full spring compression is linearly proportional to the deflection value of said full spring compression—in which case the desired value for said user energy can be realized by choosing the proper said deflection value (within the limits of how thick said compressible sole can practically be, of course).
 46. The optimal spring system of claim 45 wherein said optimal force curve method comprises a precise tuning method which requires that said optimal sole energy is defined for the case when said sole energy at full compression is used as the target value for the manufacture of said optimal spring system for a particular user, wherein this means that said footwear is precisely tuned for said user for his or her chosen impact energy for the corresponding chosen gait.
 47. The optimal spring system of claim 46 wherein said precise tuning method further comprises a precise manufacture means to realize a precise value of said optimal sole energy by simply slicing the elements of said optimal spring system to a precise value, wherein said arch spring types and said enhanced arch springs of which said optimal spring system are made are 2D springs which are uniform across their widths, wherein the spring strength of said 2D springs is determined by their widths so precise a manufacture means is easily achieved, wherein for a given shoe size there can be a multiplicity of said spring strengths for a range of said user energy values for diverse said users.
 48. The optimal spring system of claim 46 wherein said precise tuning method further comprises the manufacture of changeable said 2D springs which can be removed from and inserted into said tuned spring system, wherein said 2D springs are easy to manufacture as changeable springs.
 49. The optimal spring system of claim 46 wherein said a precise tuning method further comprises an impact force means to measure the ground reaction force of running or walking, wherein said impact force means further comprises the user's weight, the user's gait range, and measurement results from a force platform test.
 50. The optimal spring system of claim 46 wherein said a precise tuning method further comprises a gear change mechanism, wherein the term gear change means that the spring stiffness of said tuned spring system is reset after every step so that there is close to full compression of said compressible sole on a continuous basis.
 51. A gear change mechanism in a shoe which comprises a shoe upper, a footplate, a compressible sole, and a gear change spring system, wherein said gear change mechanism comprises gear springs, an outside spring section of said compressible sole which is not directly under the foot of the user of said shoe and which uses said gear springs, an underfoot spring section of said compressible sole which is directly under the foot of the user of said shoe and which uses said gear springs, one or more outside springs in said outside spring section, one or more underfoot springs in said underfoot section, wherein said underfoot springs are necessarily always compressed when said compressible sole is compressed, and one or more outside springs, and an outside spring engagement/disengagement mechanism for the purpose of engaging or disengaging said outside springs, wherein said user can be a human or a robot, wherein the human applications are normal, orthotics and prosthetics.
 52. The gear change mechanism of claim 51 wherein when said user is a robot with a robotic foot said outside springs can comprise a centrally located section located in the center region of said robotic foot, wherein this is because said robotic foot can be divided into sections which do not fully and continuously cover said robotic foot, which is not the case for a human foot, wherein said compressible sole of said robotic foot can be compressed without said centrally located section being compressed.
 53. The gear change mechanism of claim 51 wherein said outside springs and said underfoot springs are 2D springs, wherein said 2D springs are uniform across their widths so that they can be considered 2D springs, wherein the spring strength of said 2D springs is linearly proportional to their widths, wherein said spring strength can be very precisely selected, wherein said 2D springs can be rotated about shafts which extend across their widths from side to side, wherein said 2D springs can be sliced in any plane perpendicular to said shaft, wherein said 2D planes are also known as slicing planes.
 54. The gear change mechanism of claim 51 wherein side spring engagement/disengagement mechanism comprises a local force means to measure the ground reaction force of walking or running, wherein said local force means is located on said tuned shoe, a microprocessor located on said shoe, an actuator assembly, an electrical connection means to electrically connect said local force means, said microprocessor, and said actuator assembly, one or more sliced outside side springs, and one or more engageable spring drive bars each of which engages and drives a particular one of said sliced outside springs, wherein if a particular one of said sliced outside springs is not instructed by said microprocessor to engage, then it is disengaged, wherein the output of said local force means is transmitted to said microprocessor right after toe-off of said tuned shoe, whereupon said microprocessor transmits its output to said actuator assembly telling it which engageable spring drive bars are to be engaged for the next step of said shoe, wherein the optimum number of said sliced outside springs is engaged for every next step based on the measured ground force of the previous step, wherein said compressible sole approximately achieves close to full compression on every step.
 55. The gear change mechanism of claim 54 wherein said local force means is a force sensor positioned at the bottom of said compressible sole.
 56. The gear change mechanism of claim 54 wherein said engageable spring drive bar comprises a spring frame, a drive shaft oriented in the sideways direction, one or more drive bars oriented vertically, a lock hole oriented in the front/back (lengthwise) direction in the top of said drive bar, one or more bar holes oriented in the sideways direction, wherein each said bar hole is in the top of each of said drive bar, wherein said bar hole is oriented perpendicular to said lock hole, a housing, a shaft bar, one or more lock shafts each of which is positioned directly in front of said lock hole in said drive bar so that said lock shaft moves through said lock hole as said length actuator moves said shaft bar in the lengthwise direction, a length actuator oriented in the front/back direction, wherein said housing houses said length actuator, wherein said shaft bar is rigidly attached to the moving end of said length actuator, wherein said lock shafts are rigidly attached to said shaft bar and oriented in the front/back direction, wherein said spring frame is rigidly attached to the side of said footplate and extends upward to rigidly connect to said drive shaft which extends out toward the side of said compressible sole, wherein one or more of said drive bars is rotatably connected to said drive shaft via said bar hole and said drive bar hangs down from said drive shaft, wherein each said drive bar is located directly above said side sliced spring, wherein each said lock shaft is rigidly attached to one said shaft bar at staggered lengths so that each of them passes through its respective said lock hole (in said drive bar) at different times as said shaft bar is moved forward and backward by said length actuator, wherein when said lock shaft enters said lock hole, said drive bar is prevented from rotating out of the way of side sliced spring, in which case said drive bar drives said side sliced spring downward to its compressed state, wherein when said lock shaft does not pass through said lock hole then drive bar is free to rotate out of the way of said side sliced spring and said side spring engagement/disengagement mechanism has disengaged said side sliced spring from being compressed, wherein said gear change mechanism automatically changes gears so that it continuously ensures close to full compression of said compressible sole.
 57. The optimal spring system of claim 34 wherein said tension band is made of a continuous wave composite (CWC), wherein said CWC comprises multiple layers which are laid down in sinusoidal waves transversely oriented within the plane of each layer, wherein said tension band of said CWC can be stretched considerably without breaking the fibers, wherein said tension band of said CWC has very low energy hysteresis loss of the order of 1-2%.
 58. The optimal spring system of claim 37 wherein the pair of said link-spread curved springs are replaced by a pair of tension bands made of a continuous wave composite (CWC), wherein said CWC comprises multiple layers which are laid down in sinusoidal waves transversely oriented within the plane of each layer, wherein said tension band of said CWC can be stretched considerably without breaking the fibers, wherein said tension band of said CWC has very low energy hysteresis loss of the order of 1-2%.
 59. The optimized shoe of claim 1 wherein said spring system comprises an assembly of one or more component springs located anywhere under the foot or outside of the foot wherein each said component spring has its own distinct stiffness value and force curve, wherein the decision on how to use each component spring in the assembly depends on considerations of structural optimization, stability, and functionality issues such as pronation, wherein said component springs may be held together one to the other by bridging plates to form an insertable cartridge.
 60. The optimized shoe of claim 59 wherein said component spring can be oriented at any angle. 